NCERT Solutions for Class 8 Maths Chapter 10

Question 1:

Answer:

$(i) CP = Rs . 620 SP = Rs . 713 Since SP > CP, there is a gain . Gain = 713 - 620 = Rs . 93 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{93}{620} \times 100) % = 15 %$

(ii)
$CP = Rs 675 SP = Rs 630 Since SP < CP, there is a loss . Loss = 675 - 630 = Rs . 45 Loss percentage = (\frac{Loss}{CP} \times 100) % = (\frac{45}{675} \times 100) % = 6 \frac{2}{3} %$

(iii)
$CP = Rs . 345 SP = Rs . 372.60 Since SP > CP, there is a gain . Gain = 372.60 - 345 = Rs . 27.6 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{27.6}{345} \times 100) % = (\frac{2760}{345}) % = 8 %$

(iv)
$CP = Rs 80 SP = Rs 76.80 Since SP < CP, there is a loss . Loss = 80 - 76.80 = Rs . 3.2 Loss percentage = (\frac{loss}{CP} \times 100) % = (\frac{3.2}{80} \times 100) % = (\frac{32}{80} \times 100) % = 4 %$

Question 2:

$(i) CP = Rs . 620 SP = Rs . 713 Since SP > CP, there is a gain . Gain = 713 - 620 = Rs . 93 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{93}{620} \times 100) % = 15 %$

(ii)
$CP = Rs 675 SP = Rs 630 Since SP < CP, there is a loss . Loss = 675 - 630 = Rs . 45 Loss percentage = (\frac{Loss}{CP} \times 100) % = (\frac{45}{675} \times 100) % = 6 \frac{2}{3} %$

(iii)
$CP = Rs . 345 SP = Rs . 372.60 Since SP > CP, there is a gain . Gain = 372.60 - 345 = Rs . 27.6 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{27.6}{345} \times 100) % = (\frac{2760}{345}) % = 8 %$

(iv)
$CP = Rs 80 SP = Rs 76.80 Since SP < CP, there is a loss . Loss = 80 - 76.80 = Rs . 3.2 Loss percentage = (\frac{loss}{CP} \times 100) % = (\frac{3.2}{80} \times 100) % = (\frac{32}{80} \times 100) % = 4 %$

Answer:

(i)
$CP = Rs . 1650 Gain percentage = 4 % SP = \frac{(100 + gain %)}{100} \times CP = \frac{(100 + 4)}{100} \times 1650 = \frac{104 \times 1650}{100} = Rs . 1716$

(ii)
$CP = Rs . 915 Gain percentage = 6 \frac{2}{3} % = \frac{20}{3} % SP = \frac{(100 + gain %)}{100} \times CP = \frac{(100 + \frac{20}{3})}{100} \times 915 = \frac{(\frac{320}{3})}{100} \times 915 = (\frac{320}{3}) \times (\frac{1}{100}) \times 915 = Rs . 976$

(iii)
$CP = Rs . 875 Loss percentage = 12 % SP = \frac{(100 - loss %)}{100} \times CP = \frac{(100 - 12)}{100} \times 875 = \frac{77000}{100} = Rs . 770$

(iv)

$CP = Rs . 645 Loss percentage = 13 \frac{1}{3} % = \frac{40}{3} % SP = \frac{(100 - loss %)}{100} \times CP = \frac{(100 - \frac{40}{3})}{100} \times 645 = \frac{(\frac{300 - 40}{3})}{100} \times 645 = (\frac{260}{3}) \times (\frac{1}{100}) \times 645 = Rs . 559$

Question 3:

(i)
$CP = Rs . 1650 Gain percentage = 4 % SP = \frac{(100 + gain %)}{100} \times CP = \frac{(100 + 4)}{100} \times 1650 = \frac{104 \times 1650}{100} = Rs . 1716$

(ii)
$CP = Rs . 915 Gain percentage = 6 \frac{2}{3} % = \frac{20}{3} % SP = \frac{(100 + gain %)}{100} \times CP = \frac{(100 + \frac{20}{3})}{100} \times 915 = \frac{(\frac{320}{3})}{100} \times 915 = (\frac{320}{3}) \times (\frac{1}{100}) \times 915 = Rs . 976$

(iii)
$CP = Rs . 875 Loss percentage = 12 % SP = \frac{(100 - loss %)}{100} \times CP = \frac{(100 - 12)}{100} \times 875 = \frac{77000}{100} = Rs . 770$

(iv)

$CP = Rs . 645 Loss percentage = 13 \frac{1}{3} % = \frac{40}{3} % SP = \frac{(100 - loss %)}{100} \times CP = \frac{(100 - \frac{40}{3})}{100} \times 645 = \frac{(\frac{300 - 40}{3})}{100} \times 645 = (\frac{260}{3}) \times (\frac{1}{100}) \times 645 = Rs . 559$

Answer:

$(i) SP = Rs . 1596 Gain percentage = 12 % CP = \frac{100}{(100 + gain %)} \times SP = \frac{100}{(100 + 12)} \times 1596 = Rs . 1425$

(ii)

$SP = Rs . 2431 Loss percentage = 6 \frac{1}{2} % = \frac{13}{2} % CP = \frac{100}{(100 - loss %)} \times SP = \frac{100}{(100 - \frac{13}{2})} \times 2431 = \frac{100 \times 2}{187} \times 2431 = Rs . 2600$

(iii)
$SP = Rs . 657.60 Loss percentage = 4 % CP = \frac{100}{(100 - loss %)} \times SP = \frac{100}{(100 - 4)} \times 657.60 = Rs . 685$

(iv)
$SP = Rs . 34.40 Gain percentage = 7 \frac{1}{2} % = \frac{15}{2} % CP = \frac{100}{(100 + gain %)} \times SP = \frac{100}{(100 + \frac{15}{2})} \times 34.40 = \frac{100 \times 2}{215} \times 34.40 = Rs . 32$

Question 4:

$(i) SP = Rs . 1596 Gain percentage = 12 % CP = \frac{100}{(100 + gain %)} \times SP = \frac{100}{(100 + 12)} \times 1596 = Rs . 1425$

(ii)

$SP = Rs . 2431 Loss percentage = 6 \frac{1}{2} % = \frac{13}{2} % CP = \frac{100}{(100 - loss %)} \times SP = \frac{100}{(100 - \frac{13}{2})} \times 2431 = \frac{100 \times 2}{187} \times 2431 = Rs . 2600$

(iii)
$SP = Rs . 657.60 Loss percentage = 4 % CP = \frac{100}{(100 - loss %)} \times SP = \frac{100}{(100 - 4)} \times 657.60 = Rs . 685$

(iv)
$SP = Rs . 34.40 Gain percentage = 7 \frac{1}{2} % = \frac{15}{2} % CP = \frac{100}{(100 + gain %)} \times SP = \frac{100}{(100 + \frac{15}{2})} \times 34.40 = \frac{100 \times 2}{215} \times 34.40 = Rs . 32$

Answer:

CP of the iron safe = â‚¹12,160
Money spent on transportation = â‚¹340
Total CP = â‚¹12,160 + â‚¹340 = â‚¹12,500
SP of the iron safe = â‚¹12,875
Profit = SP − CP = â‚¹12,875 − â‚¹12,500 = â‚¹375
∴ Profit% = $\frac{Profit}{CP} \times 100 %$ $= \frac{375}{12500} \times 100 % = 3 %$

Question 5:

CP of the iron safe = â‚¹12,160
Money spent on transportation = â‚¹340
Total CP = â‚¹12,160 + â‚¹340 = â‚¹12,500
SP of the iron safe = â‚¹12,875
Profit = SP − CP = â‚¹12,875 − â‚¹12,500 = â‚¹375
∴ Profit% = $\frac{Profit}{CP} \times 100 %$ $= \frac{375}{12500} \times 100 % = 3 %$

Answer:

$CP of the car = Rs . 73500 Repairs = Rs . 10300 Insurance = Rs . 2600 Total CP = 73500 + 10300 + 2600 = Rs . 86400 SP = Rs . 84240 Since SP < CP, Robin has a loss . Loss = 86400 - 84240 = Rs . 2160 Loss percentage = (\frac{loss}{total CP} \times 100) % = (\frac{2160}{86400} \times 100) % = 2 \frac{1}{2} %$

Question 6:

$CP of the car = Rs . 73500 Repairs = Rs . 10300 Insurance = Rs . 2600 Total CP = 73500 + 10300 + 2600 = Rs . 86400 SP = Rs . 84240 Since SP < CP, Robin has a loss . Loss = 86400 - 84240 = Rs . 2160 Loss percentage = (\frac{loss}{total CP} \times 100) % = (\frac{2160}{86400} \times 100) % = 2 \frac{1}{2} %$

Answer:

Total cost of rice of 1st variety = â‚¹36/kg × 20 kg = â‚¹720
Total cost of rice of 2nd variety = â‚¹32/kg × 25 kg = â‚¹800
Total cost of the two rice varieties = â‚¹720 + â‚¹800 = â‚¹1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = â‚¹38/kg × 45 kg = â‚¹1,710
Gain = SP − CP = â‚¹1,710 − â‚¹1,520 = â‚¹190
Gain% = $\frac{Gain}{CP} \times 100 % = \frac{190}{1520} \times 100 % = 12 \frac{1}{2} %$

Question 7:

Total cost of rice of 1st variety = â‚¹36/kg × 20 kg = â‚¹720
Total cost of rice of 2nd variety = â‚¹32/kg × 25 kg = â‚¹800
Total cost of the two rice varieties = â‚¹720 + â‚¹800 = â‚¹1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = â‚¹38/kg × 45 kg = â‚¹1,710
Gain = SP − CP = â‚¹1,710 − â‚¹1,520 = â‚¹190
Gain% = $\frac{Gain}{CP} \times 100 % = \frac{190}{1520} \times 100 % = 12 \frac{1}{2} %$

Answer:

$Let 5 kg of coffee be mixed with 2 kg of chicory . CP of the mixture = Rs (250 \times 5 + 75 \times 2) = Rs (1250 + 150) = Rs . 1400 SP of the mixture = Rs (7 \times 230) = Rs . 1610 Since SP > CP, there is a gain . Now, gain = Rs (1610 - 1400) = Rs . 210 Gain percentage = (\frac{gain}{total CP} \times 100) % = (\frac{210}{1400} \times 100) % = 15 %$

Question 8:

$Let 5 kg of coffee be mixed with 2 kg of chicory . CP of the mixture = Rs (250 \times 5 + 75 \times 2) = Rs (1250 + 150) = Rs . 1400 SP of the mixture = Rs (7 \times 230) = Rs . 1610 Since SP > CP, there is a gain . Now, gain = Rs (1610 - 1400) = Rs . 210 Gain percentage = (\frac{gain}{total CP} \times 100) % = (\frac{210}{1400} \times 100) % = 15 %$

Answer:

$Let Rs x be the SP of each bottle and Rs y be the CP of each bottle . SP of 16 bottles = CP of 17 bottles \Rightarrow 16 x = 17 y \Rightarrow \frac{x}{y} = \frac{17}{16} Gain per bottle = SP - CP = Rs (x - y) ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{x - y}{y} \times 100) % = {(\frac{x}{y} - 1) \times 100} % = {(\frac{17}{16} - 1) \times 100} % = (\frac{1}{16} \times 100) % = 6 \frac{1}{4} %$

Question 9:

$Let Rs x be the SP of each bottle and Rs y be the CP of each bottle . SP of 16 bottles = CP of 17 bottles \Rightarrow 16 x = 17 y \Rightarrow \frac{x}{y} = \frac{17}{16} Gain per bottle = SP - CP = Rs (x - y) ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{x - y}{y} \times 100) % = {(\frac{x}{y} - 1) \times 100} % = {(\frac{17}{16} - 1) \times 100} % = (\frac{1}{16} \times 100) % = 6 \frac{1}{4} %$

Answer:

$Let Rs x be the CP of one candle and Rs . y be the SP of one candle . Now, CP of 12 candles = SP of 15 candles \Rightarrow 12 x = 15 y \Rightarrow \frac{y}{x} = \frac{12}{15} Loss = CP - SP = Rs (x - y) ∴ Loss percentage = (\frac{loss}{CP} \times 100) % = {(\frac{x - y}{x}) \times 100} % = {(1 - \frac{y}{x}) \times 100} % = {(1 - \frac{12}{15}) \times 100} % = (\frac{3}{15} \times 100) % = 20 %$

Question 10:

$Let Rs x be the CP of one candle and Rs . y be the SP of one candle . Now, CP of 12 candles = SP of 15 candles \Rightarrow 12 x = 15 y \Rightarrow \frac{y}{x} = \frac{12}{15} Loss = CP - SP = Rs (x - y) ∴ Loss percentage = (\frac{loss}{CP} \times 100) % = {(\frac{x - y}{x}) \times 100} % = {(1 - \frac{y}{x}) \times 100} % = {(1 - \frac{12}{15}) \times 100} % = (\frac{3}{15} \times 100) % = 20 %$

Answer:

It is given that,
Gain = SP of 5 cassettes                 .....(1)
Gain = SP of 130 cassettes − CP of 130 cassettes
⇒ SP of 5 cassettes = SP of 130 cassettes − CP of 130 cassettes [From (1)]
⇒ CP of 130 cassettes = SP of 125 cassettes          .....(2)
Let the CP of 1 cassettte be â‚¹x.
∴ CP of 125 cassettes = â‚¹125x
CP of 130 cassettes = â‚¹130x
SP of 125 cassettes = CP of 130 cassettes                    [From (2)]
⇒ SP of 125 cassettes = â‚¹130x
Now, gain% $= \frac{SP - CP}{CP} \times 100 % = \frac{(130 x - 125 x)}{125 x} \times 100 %$ $= \frac{5 x}{125 x} \times 100 % = 4 %$
Thus, the gain percent is 4%.

Question 11:

It is given that,
Gain = SP of 5 cassettes                 .....(1)
Gain = SP of 130 cassettes − CP of 130 cassettes
⇒ SP of 5 cassettes = SP of 130 cassettes − CP of 130 cassettes [From (1)]
⇒ CP of 130 cassettes = SP of 125 cassettes          .....(2)
Let the CP of 1 cassettte be â‚¹x.
∴ CP of 125 cassettes = â‚¹125x
CP of 130 cassettes = â‚¹130x
SP of 125 cassettes = CP of 130 cassettes                    [From (2)]
⇒ SP of 125 cassettes = â‚¹130x
Now, gain% $= \frac{SP - CP}{CP} \times 100 % = \frac{(130 x - 125 x)}{125 x} \times 100 %$ $= \frac{5 x}{125 x} \times 100 % = 4 %$
Thus, the gain percent is 4%.

Answer:

$Let Rs x be the SP of one lemon . SP of 45 lemons = Rs . 45 x Loss = SP of 3 lemons = Rs . 3 x But loss = CP - SP CP = loss + SP = 3 x + 45 x = Rs . 48 x ∴ Loss percentage = (\frac{loss}{CP} \times 100) % = (\frac{3 x}{48 x} \times 100) % = 6 \frac{1}{4} %$

Question 12:

$Let Rs x be the SP of one lemon . SP of 45 lemons = Rs . 45 x Loss = SP of 3 lemons = Rs . 3 x But loss = CP - SP CP = loss + SP = 3 x + 45 x = Rs . 48 x ∴ Loss percentage = (\frac{loss}{CP} \times 100) % = (\frac{3 x}{48 x} \times 100) % = 6 \frac{1}{4} %$

Answer:

LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = â‚¹20
So, CP of 1 orange = $\frac{20}{6} = ₹ \frac{10}{3}$
CP of 12 orange = $12 \times \frac{10}{3} = ₹ 40$
SP of 4 oranges = â‚¹18
SP of 1 orange = $\frac{18}{4} = ₹ \frac{9}{2}$
SP of 12 oranges = $12 \times \frac{9}{2} = ₹ 54$
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP − CP = â‚¹54 − â‚¹40 = â‚¹14
∴ Profit% = $\frac{Profit}{CP} \times 100 % = \frac{14}{40} \times 100 % = 35 %$

Question 13:

LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = â‚¹20
So, CP of 1 orange = $\frac{20}{6} = ₹ \frac{10}{3}$
CP of 12 orange = $12 \times \frac{10}{3} = ₹ 40$
SP of 4 oranges = â‚¹18
SP of 1 orange = $\frac{18}{4} = ₹ \frac{9}{2}$
SP of 12 oranges = $12 \times \frac{9}{2} = ₹ 54$
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP − CP = â‚¹54 − â‚¹40 = â‚¹14
∴ Profit% = $\frac{Profit}{CP} \times 100 % = \frac{14}{40} \times 100 % = 35 %$

Answer:

LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = â‚¹40
∴ CP of 1 banana = $\frac{40}{12} = ₹ \frac{10}{3}$
⇒ CP of 60 bananas = $60 \times \frac{10}{3} = ₹ 200$
SP of 10 bananas = â‚¹36
∴ SP of 1 banana = $\frac{36}{10} = ₹ \frac{18}{5}$
⇒ SP of 60 bananas = $60 \times \frac{18}{5} = ₹ 216$
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP − CP = â‚¹216 − â‚¹200 = â‚¹16
∴ Profit% = $\frac{Profit}{CP} \times 100 % = \frac{16}{200} \times 100 = 8 %$

Question 14:

LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = â‚¹40
∴ CP of 1 banana = $\frac{40}{12} = ₹ \frac{10}{3}$
⇒ CP of 60 bananas = $60 \times \frac{10}{3} = ₹ 200$
SP of 10 bananas = â‚¹36
∴ SP of 1 banana = $\frac{36}{10} = ₹ \frac{18}{5}$
⇒ SP of 60 bananas = $60 \times \frac{18}{5} = ₹ 216$
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP − CP = â‚¹216 − â‚¹200 = â‚¹16
∴ Profit% = $\frac{Profit}{CP} \times 100 % = \frac{16}{200} \times 100 = 8 %$

Answer:

LCM of 10 and 12 = 60
Let the number of apples bought be 60.
CP of 10 oranges = â‚¹75
∴ CP of 1 orange = $₹ \frac{75}{10}$
⇒ CP of 60 orange = $60 \times \frac{75}{10} = ₹ 450$
SP of 12 oranges = â‚¹75
∴ SP of 1 orange = $₹ \frac{75}{12}$
⇒ SP of 60 oranges = $60 \times \frac{75}{12} = ₹ 375$
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP − SP = â‚¹450 − â‚¹375 = â‚¹75
∴ Loss% = $\frac{Loss}{CP} \times 100 % = \frac{75}{450} \times 100 % = 16 \frac{2}{3} %$

Question 15:

LCM of 10 and 12 = 60
Let the number of apples bought be 60.
CP of 10 oranges = â‚¹75
∴ CP of 1 orange = $₹ \frac{75}{10}$
⇒ CP of 60 orange = $60 \times \frac{75}{10} = ₹ 450$
SP of 12 oranges = â‚¹75
∴ SP of 1 orange = $₹ \frac{75}{12}$
⇒ SP of 60 oranges = $60 \times \frac{75}{12} = ₹ 375$
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP − SP = â‚¹450 − â‚¹375 = â‚¹75
∴ Loss% = $\frac{Loss}{CP} \times 100 % = \frac{75}{450} \times 100 % = 16 \frac{2}{3} %$

Answer:

Let the number of eggs purchased be x.
CP of 3 eggs = â‚¹16
∴ CP of 1 egg = $₹ \frac{16}{3}$
⇒ CP of x eggs = $₹ \frac{16}{3} x$
SP of 5 eggs = â‚¹36
∴ SP of 1 egg = $₹ \frac{36}{5}$
⇒ SP of x eggs = $₹ \frac{36}{5} x$
Gain = SP − CP = â‚¹168
$∴ \frac{36}{5} x - \frac{16}{3} x = 168 \Rightarrow \frac{28}{15} x = 168 \Rightarrow x = \frac{168 \times 15}{28} \Rightarrow x = 90$
Hence, the man purchased 90 eggs.

Question 16:

Let the number of eggs purchased be x.
CP of 3 eggs = â‚¹16
∴ CP of 1 egg = $₹ \frac{16}{3}$
⇒ CP of x eggs = $₹ \frac{16}{3} x$
SP of 5 eggs = â‚¹36
∴ SP of 1 egg = $₹ \frac{36}{5}$
⇒ SP of x eggs = $₹ \frac{36}{5} x$
Gain = SP − CP = â‚¹168
$∴ \frac{36}{5} x - \frac{16}{3} x = 168 \Rightarrow \frac{28}{15} x = 168 \Rightarrow x = \frac{168 \times 15}{28} \Rightarrow x = 90$
Hence, the man purchased 90 eggs.

Answer:

$SP of the camera = Rs . 1080 Let Rs x be the CP . Gain = Rs . \frac{1}{8} x . . . (i) Also, gain = SP - CP = Rs . (1080 - x) . . . (ii) From (i) and (ii), we have : \frac{1}{8} x = 1080 - x \Rightarrow x = 8640 - 8 x \Rightarrow 9 x = 8640 \Rightarrow x = 960 ∴ CP = Rs . 960 Now, gain = \frac{1}{8} x = \frac{960}{8} = Rs . 120 ∴ Gain percentage = (\frac{120}{960} \times 100) % = 12 \frac{1}{2} %$

Question 17:

$SP of the camera = Rs . 1080 Let Rs x be the CP . Gain = Rs . \frac{1}{8} x . . . (i) Also, gain = SP - CP = Rs . (1080 - x) . . . (ii) From (i) and (ii), we have : \frac{1}{8} x = 1080 - x \Rightarrow x = 8640 - 8 x \Rightarrow 9 x = 8640 \Rightarrow x = 960 ∴ CP = Rs . 960 Now, gain = \frac{1}{8} x = \frac{960}{8} = Rs . 120 ∴ Gain percentage = (\frac{120}{960} \times 100) % = 12 \frac{1}{2} %$

Answer:

$SP of the pen = Rs . 54 Let Rs x be the CP of the pen . Loss = Rs . \frac{x}{10} SP = CP - Loss = x - \frac{x}{10} = Rs . \frac{9 x}{10} Now, we have \frac{9 x}{10} = 54 \Rightarrow x = 54 \times \frac{10}{9} \Rightarrow x = 60 ∴ CP of the pen = Rs . 60 Now, loss = \frac{x}{10} = \frac{60}{10} = Rs . 6 ∴ Loss percentage = (\frac{loss}{CP} \times 100) % = (\frac{6}{60} \times 100) % = 10 %$

Question 18:

$SP of the pen = Rs . 54 Let Rs x be the CP of the pen . Loss = Rs . \frac{x}{10} SP = CP - Loss = x - \frac{x}{10} = Rs . \frac{9 x}{10} Now, we have \frac{9 x}{10} = 54 \Rightarrow x = 54 \times \frac{10}{9} \Rightarrow x = 60 ∴ CP of the pen = Rs . 60 Now, loss = \frac{x}{10} = \frac{60}{10} = Rs . 6 ∴ Loss percentage = (\frac{loss}{CP} \times 100) % = (\frac{6}{60} \times 100) % = 10 %$

Answer:

Let the cost price be â‚¹x.
Loss = 10% of â‚¹x = $\frac{10}{100} x = ₹ \frac{x}{10}$
SP in case of loss = CP − Loss = $x - \frac{x}{10} = ₹ \frac{9 x}{10}$
Gain =10% of â‚¹x = $\frac{10}{100} x = ₹ \frac{x}{10}$
SP in case of profit = CP + Profit = $x + \frac{x}{10} = ₹ \frac{11 x}{10}$
It is given that dealer gets â‚¹940 more if sold at a profit of 10% instead of loss of 10%.
∴ SP in case of profit − SP in case of loss = â‚¹940
$\Rightarrow \frac{11 x}{10} - \frac{9 x}{10} = 940 \Rightarrow \frac{2 x}{10} = 940 \Rightarrow x = 4700$
Hence, the cost price of the table is â‚¹4,700.

Question 19:

Let the cost price be â‚¹x.
Loss = 10% of â‚¹x = $\frac{10}{100} x = ₹ \frac{x}{10}$
SP in case of loss = CP − Loss = $x - \frac{x}{10} = ₹ \frac{9 x}{10}$
Gain =10% of â‚¹x = $\frac{10}{100} x = ₹ \frac{x}{10}$
SP in case of profit = CP + Profit = $x + \frac{x}{10} = ₹ \frac{11 x}{10}$
It is given that dealer gets â‚¹940 more if sold at a profit of 10% instead of loss of 10%.
∴ SP in case of profit − SP in case of loss = â‚¹940
$\Rightarrow \frac{11 x}{10} - \frac{9 x}{10} = 940 \Rightarrow \frac{2 x}{10} = 940 \Rightarrow x = 4700$
Hence, the cost price of the table is â‚¹4,700.

Answer:

$Let R s x b e t h e CP . {Gain}_{1} percentage = (\frac{{gain}_{1}}{CP} \times 100) % \Rightarrow 15 = \frac{{gain}_{1}}{x} \times 100 \Rightarrow {Gain}_{1} = Rs \frac{15 x}{100} Again, {gain}_{2} percentage = (\frac{{gain}_{2}}{CP} \times 100) % \Rightarrow 8 = \frac{{gain}_{2}}{x} \times 100 \Rightarrow {Gain}_{2} = Rs \frac{8 x}{100} According to the question, we have : {Gain}_{1} - {gain}_{2} = 56 \Rightarrow \frac{15 x}{100} - \frac{8 x}{100} = 56 \Rightarrow \frac{7 x}{100} = 56 \Rightarrow 7 x = 5600 \Rightarrow x = 800 Hence, the CP of the chair is Rs 800 .$

Question 20:

$Let R s x b e t h e CP . {Gain}_{1} percentage = (\frac{{gain}_{1}}{CP} \times 100) % \Rightarrow 15 = \frac{{gain}_{1}}{x} \times 100 \Rightarrow {Gain}_{1} = Rs \frac{15 x}{100} Again, {gain}_{2} percentage = (\frac{{gain}_{2}}{CP} \times 100) % \Rightarrow 8 = \frac{{gain}_{2}}{x} \times 100 \Rightarrow {Gain}_{2} = Rs \frac{8 x}{100} According to the question, we have : {Gain}_{1} - {gain}_{2} = 56 \Rightarrow \frac{15 x}{100} - \frac{8 x}{100} = 56 \Rightarrow \frac{7 x}{100} = 56 \Rightarrow 7 x = 5600 \Rightarrow x = 800 Hence, the CP of the chair is Rs 800 .$

Answer:

Let the CP be â‚¹x.
SP when gain is 10% = $x + \frac{10}{100} x = ₹ \frac{110}{100} x$
SP when gain is 14% = $x + \frac{14}{100} x = ₹ \frac{114}{100} x$
Difference in SP = SP when gain is 14% − SP when gain is 10% = â‚¹260
$∴ \frac{114 x}{100} - \frac{110 x}{100} = 260 \Rightarrow \frac{4 x}{100} = 260 \Rightarrow x = 6500$
Hence, the CP of the cycle is â‚¹6,500.

Question 21:

Let the CP be â‚¹x.
SP when gain is 10% = $x + \frac{10}{100} x = ₹ \frac{110}{100} x$
SP when gain is 14% = $x + \frac{14}{100} x = ₹ \frac{114}{100} x$
Difference in SP = SP when gain is 14% − SP when gain is 10% = â‚¹260
$∴ \frac{114 x}{100} - \frac{110 x}{100} = 260 \Rightarrow \frac{4 x}{100} = 260 \Rightarrow x = 6500$
Hence, the CP of the cycle is â‚¹6,500.

Answer:

40 kg of wheat is bought for â‚¹12.50/kg.
∴ CP of 40 kg of wheat = 40 × 12.50 = â‚¹500
30 kg of wheat is bought for â‚¹14/kg.
∴ CP of 30 kg of wheat = 30 × 14 = â‚¹420
Total CP = â‚¹500 + â‚¹420 = â‚¹920
Profit = 5% of CP = 5% of â‚¹920 = $\frac{5}{100} \times 920 = ₹ 46$
Let the SP be â‚¹x.
Profit = SP − CP
⇒ x − 920 = 46
⇒ x = â‚¹966
SP of 70 kg wheat = â‚¹966
∴ SP of 1 kg wheat = $\frac{966}{70} = ₹ 13.80$
Thus, the selling price of the mixture is â‚¹13.80/kg.

Question 22:

40 kg of wheat is bought for â‚¹12.50/kg.
∴ CP of 40 kg of wheat = 40 × 12.50 = â‚¹500
30 kg of wheat is bought for â‚¹14/kg.
∴ CP of 30 kg of wheat = 30 × 14 = â‚¹420
Total CP = â‚¹500 + â‚¹420 = â‚¹920
Profit = 5% of CP = 5% of â‚¹920 = $\frac{5}{100} \times 920 = ₹ 46$
Let the SP be â‚¹x.
Profit = SP − CP
⇒ x − 920 = 46
⇒ x = â‚¹966
SP of 70 kg wheat = â‚¹966
∴ SP of 1 kg wheat = $\frac{966}{70} = ₹ 13.80$
Thus, the selling price of the mixture is â‚¹13.80/kg.

Answer:

CP of the first bat = â‚¹840
Profit% on the first bat = 15%
∴ Profit = 15% of â‚¹840 = $\frac{15}{100} \times 840 = ₹ 126$
SP of the first bat = â‚¹840 + â‚¹126 = â‚¹966
CP of the second bat = â‚¹360
Loss = 5% of â‚¹360 = $\frac{5}{100} \times 360 = ₹ 18$
SP of the second bat = â‚¹360 − â‚¹18 = â‚¹342
Total CP of two bats = CP of first bat + CP of second bat = â‚¹840 + â‚¹360 = â‚¹1,200
Total SP of two bats = SP of first bat + SP of second bat = â‚¹966 + â‚¹342 = â‚¹1,308
Here, Total SP of two bats > Total CP of two bats.
Gain = Total SP of two bats − Total CP of two bats = â‚¹1,308 − â‚¹1,200 = â‚¹108
∴ Gain% in the whole transaction $= \frac{Gain}{Total CP of two bats} \times 100 %$ $= \frac{108}{1200} \times 100 = 9 %$

Question 23:

CP of the first bat = â‚¹840
Profit% on the first bat = 15%
∴ Profit = 15% of â‚¹840 = $\frac{15}{100} \times 840 = ₹ 126$
SP of the first bat = â‚¹840 + â‚¹126 = â‚¹966
CP of the second bat = â‚¹360
Loss = 5% of â‚¹360 = $\frac{5}{100} \times 360 = ₹ 18$
SP of the second bat = â‚¹360 − â‚¹18 = â‚¹342
Total CP of two bats = CP of first bat + CP of second bat = â‚¹840 + â‚¹360 = â‚¹1,200
Total SP of two bats = SP of first bat + SP of second bat = â‚¹966 + â‚¹342 = â‚¹1,308
Here, Total SP of two bats > Total CP of two bats.
Gain = Total SP of two bats − Total CP of two bats = â‚¹1,308 − â‚¹1,200 = â‚¹108
∴ Gain% in the whole transaction $= \frac{Gain}{Total CP of two bats} \times 100 %$ $= \frac{108}{1200} \times 100 = 9 %$

Answer:

CP of first jeans = â‚¹1,450
Profit = 8% of CP = $\frac{8}{100} \times 1450 = ₹ 116$
SP of first jeans = â‚¹1,450 + â‚¹116 = â‚¹1,566
CP of second jeans = â‚¹1,450
Loss = 4% of CP = $\frac{4}{100} \times 1450 = ₹ 58$
SP of second jeans = â‚¹1450 − â‚¹58 = â‚¹1,392
Total CP of two jeans = CP of first jeans + CP of second jeans = â‚¹1,450 + â‚¹1,450 = â‚¹2,900
Total SP of two jeans = SP of first jeans + SP of second jeans = â‚¹1,566 + â‚¹1,392 = â‚¹2,958
Here, Total SP of two jeans > Total CP of two jeans.
Gain = Total SP of two jeans − Total CP of two jeans = â‚¹2,958 − â‚¹2,900 = â‚¹58
∴ Gain% = $\frac{Gain}{Total CP of two jeans} \times 100 % = \frac{58}{2900} \times 100 % = 2 %$

Question 24:

CP of first jeans = â‚¹1,450
Profit = 8% of CP = $\frac{8}{100} \times 1450 = ₹ 116$
SP of first jeans = â‚¹1,450 + â‚¹116 = â‚¹1,566
CP of second jeans = â‚¹1,450
Loss = 4% of CP = $\frac{4}{100} \times 1450 = ₹ 58$
SP of second jeans = â‚¹1450 − â‚¹58 = â‚¹1,392
Total CP of two jeans = CP of first jeans + CP of second jeans = â‚¹1,450 + â‚¹1,450 = â‚¹2,900
Total SP of two jeans = SP of first jeans + SP of second jeans = â‚¹1,566 + â‚¹1,392 = â‚¹2,958
Here, Total SP of two jeans > Total CP of two jeans.
Gain = Total SP of two jeans − Total CP of two jeans = â‚¹2,958 − â‚¹2,900 = â‚¹58
∴ Gain% = $\frac{Gain}{Total CP of two jeans} \times 100 % = \frac{58}{2900} \times 100 % = 2 %$

Answer:

CP of 1 kg of rice = Rs 25
C.P of 200 kg rice= $Rs (200 \times 25) = Rs 5000$
CP of 80 kg of rice= $Rs (25 \times 80) = Rs 2000$

CP of 40 kg of rice = $Rs (25 \times 40) = Rs 1000$

$SP of 80 kg of rice = \frac{100 + gain %}{100} \times CP = Rs \frac{110}{100} \times 2000 = Rs 2200$

$SP of 40 kg rice = \frac{100 - loss %}{100} \times CP = Rs \frac{96}{100} \times 1000 = Rs 960$

$SP of 200 kg rice = \frac{100 + gain %}{100} \times CP = Rs \frac{108}{100} \times 5000 = Rs 5400$

Remaining quantity of rice = (200 − 80 + 40) kg = 80 kg

â€‹SP of the remaining rice (80 kg) = Rs (5400 − 2200 − 960)
= Rs 2240

$∴ Rate per kg = Rs \frac{2240}{80} = Rs 28$

Question 25:

CP of 1 kg of rice = Rs 25
C.P of 200 kg rice= $Rs (200 \times 25) = Rs 5000$
CP of 80 kg of rice= $Rs (25 \times 80) = Rs 2000$

CP of 40 kg of rice = $Rs (25 \times 40) = Rs 1000$

$SP of 80 kg of rice = \frac{100 + gain %}{100} \times CP = Rs \frac{110}{100} \times 2000 = Rs 2200$

$SP of 40 kg rice = \frac{100 - loss %}{100} \times CP = Rs \frac{96}{100} \times 1000 = Rs 960$

$SP of 200 kg rice = \frac{100 + gain %}{100} \times CP = Rs \frac{108}{100} \times 5000 = Rs 5400$

Remaining quantity of rice = (200 − 80 + 40) kg = 80 kg

â€‹SP of the remaining rice (80 kg) = Rs (5400 − 2200 − 960)
= Rs 2240

$∴ Rate per kg = Rs \frac{2240}{80} = Rs 28$

Answer:

Let the CP of the TV set be â‚¹x.
SP of the TV set = $\frac{6}{5} CP = ₹ \frac{6}{5} x$
Gain = SP of the TV set − CP of the TV set = $\frac{6}{5} x - x = ₹ \frac{x}{5}$
Gain% = $\frac{Gain}{CP} \times 100 % = \frac{\frac{x}{5}}{x} \times 100 % = \frac{100}{5} % = 20 %$

Question 26:

Let the CP of the TV set be â‚¹x.
SP of the TV set = $\frac{6}{5} CP = ₹ \frac{6}{5} x$
Gain = SP of the TV set − CP of the TV set = $\frac{6}{5} x - x = ₹ \frac{x}{5}$
Gain% = $\frac{Gain}{CP} \times 100 % = \frac{\frac{x}{5}}{x} \times 100 % = \frac{100}{5} % = 20 %$

Answer:

Let the CP of the flower vase set be â‚¹x.
SP of the flower vase = $\frac{5}{6} CP = ₹ \frac{5}{6} x$
Loss = CP − SP = $x - \frac{5}{6} x = ₹ \frac{x}{6}$
Loss% = $\frac{Loss}{CP} \times 100 % = \frac{\frac{x}{6}}{x} \times 100 % = \frac{100}{6} % = \frac{50}{3} % = 16 \frac{2}{3} %$

Question 27:

Let the CP of the flower vase set be â‚¹x.
SP of the flower vase = $\frac{5}{6} CP = ₹ \frac{5}{6} x$
Loss = CP − SP = $x - \frac{5}{6} x = ₹ \frac{x}{6}$
Loss% = $\frac{Loss}{CP} \times 100 % = \frac{\frac{x}{6}}{x} \times 100 % = \frac{100}{6} % = \frac{50}{3} % = 16 \frac{2}{3} %$

Answer:

SP of the bouquet = Rs 322
Gain percentage = 15%
$CP of the bouquet = (\frac{100}{100 + gain %}) \times SP = Rs (\frac{100}{100 + 15}) \times 322 = Rs \frac{100}{115} \times 322 = Rs 280$

Now, CP = Rs 128 and desired gain percentage = 25%

$∴ Desired S P = (\frac{100 + gain %}{100}) \times CP = Rs \frac{125}{100} \times 280 = Rs 350$

â€‹Hence, the selling price to obtain the desired gain must be Rs 350.

Question 28:

SP of the bouquet = Rs 322
Gain percentage = 15%
$CP of the bouquet = (\frac{100}{100 + gain %}) \times SP = Rs (\frac{100}{100 + 15}) \times 322 = Rs \frac{100}{115} \times 322 = Rs 280$

Now, CP = Rs 128 and desired gain percentage = 25%

$∴ Desired S P = (\frac{100 + gain %}{100}) \times CP = Rs \frac{125}{100} \times 280 = Rs 350$

â€‹Hence, the selling price to obtain the desired gain must be Rs 350.

Answer:

Let the CP of the umbrella be â‚¹x.
SP of the umbrella = â‚¹336
Loss = 4% of â‚¹x = $₹ \frac{4}{100} x$
CP − Loss = SP
$\Rightarrow x - \frac{4}{100} x = 336 \Rightarrow \frac{96}{100} x = 336 \Rightarrow x = ₹ 350$
∴ CP of the umbrella = â‚¹350
Now, for gain of 4%,
SP = CP + Gain
$\Rightarrow SP = 350 + \frac{4}{100} \times 350 \Rightarrow SP = 350 + 14 \Rightarrow SP = ₹ 364$
Hence, in order to gain 4%, the umbrella should be sold for â‚¹364.

Question 29:

Let the CP of the umbrella be â‚¹x.
SP of the umbrella = â‚¹336
Loss = 4% of â‚¹x = $₹ \frac{4}{100} x$
CP − Loss = SP
$\Rightarrow x - \frac{4}{100} x = 336 \Rightarrow \frac{96}{100} x = 336 \Rightarrow x = ₹ 350$
∴ CP of the umbrella = â‚¹350
Now, for gain of 4%,
SP = CP + Gain
$\Rightarrow SP = 350 + \frac{4}{100} \times 350 \Rightarrow SP = 350 + 14 \Rightarrow SP = ₹ 364$
Hence, in order to gain 4%, the umbrella should be sold for â‚¹364.

Answer:

Let the original price be $x$ .
SP = Rs 3120
Now, SP = CP − loss
â€‹ $\Rightarrow 3120 = x - \frac{4}{\frac{100}{x}} \Rightarrow 3120 = x - \frac{x}{25} \Rightarrow 3120 = \frac{24 x}{25} \Rightarrow \frac{3120 \times 25}{24} = x \Rightarrow x = 3250$

So, the cost price is Rs 3250.

If it is sold for Rs 3445, then its a gain because SP > CP.
Now, gain = SP − CP
= Rs (3445 − 3250)
= Rs 195
$∴ G a i n p e r c e n t a g e = (\frac{g a i n}{C P} \times 100) % = (\frac{195}{3250} \times 100) % = 6 %$

Hence, gain percent = 6%

Question 30:

Let the original price be $x$ .
SP = Rs 3120
Now, SP = CP − loss
â€‹ $\Rightarrow 3120 = x - \frac{4}{\frac{100}{x}} \Rightarrow 3120 = x - \frac{x}{25} \Rightarrow 3120 = \frac{24 x}{25} \Rightarrow \frac{3120 \times 25}{24} = x \Rightarrow x = 3250$

So, the cost price is Rs 3250.

If it is sold for Rs 3445, then its a gain because SP > CP.
Now, gain = SP − CP
= Rs (3445 − 3250)
= Rs 195
$∴ G a i n p e r c e n t a g e = (\frac{g a i n}{C P} \times 100) % = (\frac{195}{3250} \times 100) % = 6 %$

Hence, gain percent = 6%

Answer:

SP of first saree = â‚¹1,980
Loss = 10%
Let the CP of first saree be â‚¹x.
CP = Loss + SP
$\Rightarrow \frac{10}{100} \times x + 1980 = x \Rightarrow x - \frac{10}{100} x = 1980 \Rightarrow \frac{90}{100} x = 1980 \Rightarrow x = 2200$
∴ CP of first saree = â‚¹2,200
SP of second saree = â‚¹1,980
Gain = 10%
Let the CP of second saree be â‚¹y.
CP = SP − Gain
$\Rightarrow 1980 - \frac{10}{100} \times y = y \Rightarrow 1980 - \frac{y}{10} = y \Rightarrow y + \frac{y}{10} = 1980 \Rightarrow \frac{11 y}{10} = 1980 \Rightarrow y = 1800$
∴ CP of second saree = â‚¹1,800
Total CP of two sarees = CP of first saree + CP of second saree = â‚¹2,200 + â‚¹1,800 = â‚¹4,000
Total SP of two sarees = SP of first saree + SP of second saree = â‚¹1,980 + â‚¹1,980 = â‚¹3,960
Here, Total CP of two sarees > Total SP of two sarees
Loss = Total CP of two sarees − Total SP of two sarees = â‚¹4,000 − â‚¹3,960 = â‚¹40
∴ Loss% in the whole transaction $= \frac{Loss}{Total CP of two sarees} \times 100 % = \frac{40}{4000} \times 100 % = 1 %$

Question 31:

SP of first saree = â‚¹1,980
Loss = 10%
Let the CP of first saree be â‚¹x.
CP = Loss + SP
$\Rightarrow \frac{10}{100} \times x + 1980 = x \Rightarrow x - \frac{10}{100} x = 1980 \Rightarrow \frac{90}{100} x = 1980 \Rightarrow x = 2200$
∴ CP of first saree = â‚¹2,200
SP of second saree = â‚¹1,980
Gain = 10%
Let the CP of second saree be â‚¹y.
CP = SP − Gain
$\Rightarrow 1980 - \frac{10}{100} \times y = y \Rightarrow 1980 - \frac{y}{10} = y \Rightarrow y + \frac{y}{10} = 1980 \Rightarrow \frac{11 y}{10} = 1980 \Rightarrow y = 1800$
∴ CP of second saree = â‚¹1,800
Total CP of two sarees = CP of first saree + CP of second saree = â‚¹2,200 + â‚¹1,800 = â‚¹4,000
Total SP of two sarees = SP of first saree + SP of second saree = â‚¹1,980 + â‚¹1,980 = â‚¹3,960
Here, Total CP of two sarees > Total SP of two sarees
Loss = Total CP of two sarees − Total SP of two sarees = â‚¹4,000 − â‚¹3,960 = â‚¹40
∴ Loss% in the whole transaction $= \frac{Loss}{Total CP of two sarees} \times 100 % = \frac{40}{4000} \times 100 % = 1 %$

Answer:

SP of first fan = â‚¹1,140
Gain = 14%
Let the CP of first fan be â‚¹x.
CP = SP − Gain
$\Rightarrow x = 1140 - \frac{14}{100} x \Rightarrow x + \frac{14}{100} x = 1140 \Rightarrow \frac{114}{100} x = 1140 \Rightarrow x = 1000$
∴ CP of first fan = â‚¹1,000
SP of second fan = â‚¹1,140
Loss = 5%
Let the CP of second fan be â‚¹y.
CP = Loss + SP
$\Rightarrow y = \frac{5}{100} y + 1140 \Rightarrow y - \frac{5}{100} y = 1140 \Rightarrow \frac{95}{100} y = 1140 \Rightarrow y = 1200$
∴ CP of second fan = â‚¹1,200
Total CP of two fans = CP of first fan + CP of second fan = â‚¹1,000 + â‚¹1,200 = â‚¹2,200
Total SP of two fans = SP of first fan + SP of second fan = â‚¹1,140 + â‚¹1,140 = â‚¹2,280
Here, Total SP of two fans > Total CP of two fans
Gain = Total SP of two fans − Total CP of two fans = â‚¹2,280 − â‚¹2,200 = â‚¹80
∴ Gain% on whole transaction $= \frac{Gain}{Total CP of two fans} \times 100 % = \frac{80}{2200} \times 100 % = 3.64 %$

Question 32:

SP of first fan = â‚¹1,140
Gain = 14%
Let the CP of first fan be â‚¹x.
CP = SP − Gain
$\Rightarrow x = 1140 - \frac{14}{100} x \Rightarrow x + \frac{14}{100} x = 1140 \Rightarrow \frac{114}{100} x = 1140 \Rightarrow x = 1000$
∴ CP of first fan = â‚¹1,000
SP of second fan = â‚¹1,140
Loss = 5%
Let the CP of second fan be â‚¹y.
CP = Loss + SP
$\Rightarrow y = \frac{5}{100} y + 1140 \Rightarrow y - \frac{5}{100} y = 1140 \Rightarrow \frac{95}{100} y = 1140 \Rightarrow y = 1200$
∴ CP of second fan = â‚¹1,200
Total CP of two fans = CP of first fan + CP of second fan = â‚¹1,000 + â‚¹1,200 = â‚¹2,200
Total SP of two fans = SP of first fan + SP of second fan = â‚¹1,140 + â‚¹1,140 = â‚¹2,280
Here, Total SP of two fans > Total CP of two fans
Gain = Total SP of two fans − Total CP of two fans = â‚¹2,280 − â‚¹2,200 = â‚¹80
∴ Gain% on whole transaction $= \frac{Gain}{Total CP of two fans} \times 100 % = \frac{80}{2200} \times 100 % = 3.64 %$

Answer:

Let the CP of the watch for Vinod be â‚¹x.
SP = Gain + CP
$= 12 % of CP + x = \frac{12}{100} x + x = ₹ \frac{112}{100} x$
Now,
SP of the water for Vinod will be the CP of the watch for Arun.
SP of the watch for Arun
= CP − Loss
$= \frac{112}{100} x - 5 % of \frac{112}{100} x = \frac{112}{100} x - \frac{5}{100} (\frac{112}{100} x) = \frac{112}{100} x (1 - \frac{5}{100}) = ₹ \frac{112}{100} x (\frac{95}{100})$
SP of the watch for Arun will be the CP of the watch for Manoj.
But, CP of the watch for Manoj = â‚¹3,990
So,
$\frac{112}{100} x (\frac{95}{100}) = 3990$
$\Rightarrow x = \frac{3990 \times 100 \times 100}{112 \times 95} = 3750$
Thus, Vinod paid â‚¹3,750 for the watch.

Question 33:

Let the CP of the watch for Vinod be â‚¹x.
SP = Gain + CP
$= 12 % of CP + x = \frac{12}{100} x + x = ₹ \frac{112}{100} x$
Now,
SP of the water for Vinod will be the CP of the watch for Arun.
SP of the watch for Arun
= CP − Loss
$= \frac{112}{100} x - 5 % of \frac{112}{100} x = \frac{112}{100} x - \frac{5}{100} (\frac{112}{100} x) = \frac{112}{100} x (1 - \frac{5}{100}) = ₹ \frac{112}{100} x (\frac{95}{100})$
SP of the watch for Arun will be the CP of the watch for Manoj.
But, CP of the watch for Manoj = â‚¹3,990
So,
$\frac{112}{100} x (\frac{95}{100}) = 3990$
$\Rightarrow x = \frac{3990 \times 100 \times 100}{112 \times 95} = 3750$
Thus, Vinod paid â‚¹3,750 for the watch.

Answer:

CP of the plot of land = â‚¹4,80,000
CP of $\frac{2}{5}$ th of the land = $\frac{2}{5} \times 480000 = ₹ 1, 92, 000$
Loss on $\frac{2}{5}$ th of the land = 6%
SP of $\frac{2}{5}$ th of the land = CP − Loss
$= 192000 - \frac{6}{100} \times 192000 = ₹ 1, 80, 480$
CP of $\frac{3}{5}$ th of the land = 480000 − 192000 = â‚¹2,88,000
Total gain% = 10%
Total gain = $\frac{10}{100} \times 480000 = ₹ 48, 000$
Total SP = CP + Gain = â‚¹4,80,000 + â‚¹48,000 = â‚¹5,28,000
SP of $\frac{3}{5}$ th of the land = â‚¹5,28,000 − â‚¹1,80,480 = â‚¹3,47,520
Gain on $\frac{3}{5}$ th of the land = SP of $\frac{3}{5}$ th land − CP of $\frac{3}{5}$ th land
= â‚¹3,47,520 − â‚¹2,88,000
= â‚¹59,520
Gain% on seling the remaining part of the plot = $\frac{Gain}{CP of \frac{3}{5} th land} \times 100 % = \frac{59520}{288000} \times 100 % = 20 \frac{2}{3} %$

Question 34:

CP of the plot of land = â‚¹4,80,000
CP of $\frac{2}{5}$ th of the land = $\frac{2}{5} \times 480000 = ₹ 1, 92, 000$
Loss on $\frac{2}{5}$ th of the land = 6%
SP of $\frac{2}{5}$ th of the land = CP − Loss
$= 192000 - \frac{6}{100} \times 192000 = ₹ 1, 80, 480$
CP of $\frac{3}{5}$ th of the land = 480000 − 192000 = â‚¹2,88,000
Total gain% = 10%
Total gain = $\frac{10}{100} \times 480000 = ₹ 48, 000$
Total SP = CP + Gain = â‚¹4,80,000 + â‚¹48,000 = â‚¹5,28,000
SP of $\frac{3}{5}$ th of the land = â‚¹5,28,000 − â‚¹1,80,480 = â‚¹3,47,520
Gain on $\frac{3}{5}$ th of the land = SP of $\frac{3}{5}$ th land − CP of $\frac{3}{5}$ th land
= â‚¹3,47,520 − â‚¹2,88,000
= â‚¹59,520
Gain% on seling the remaining part of the plot = $\frac{Gain}{CP of \frac{3}{5} th land} \times 100 % = \frac{59520}{288000} \times 100 % = 20 \frac{2}{3} %$

Answer:

CP of sugar = Rs 4500
Profit on one-third of the sugar = 10%

CP of one-third of the sugar = Rs $\frac{4500}{3} = Rs . 1500$

$SP of one - third of the sugar = \frac{100 + gain %}{100} \times CP = Rs \frac{110}{100} \times 1500 = Rs 1650$

Now, profit= Rs (1650 − 1500) = Rs 150

At a profit of 12%, we have:
$SP of sugar = \frac{100 + gain %}{100} \times CP = Rs \frac{112}{100} \times 4500 = Rs 5040$

∴ Gain= Rs (5040 − 4500) = Rs 5400

Profit on the remaining amount of sugar = Rs (540 − 150) = Rs 390
CP of the remaining sugar = Rs (4500 − 1500) = Rs 3000

$Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{390}{3000} \times 100) % = 13 %$

Therefore, the profit on the remaining amount of sugar is 13%.

Question 1:

CP of sugar = Rs 4500
Profit on one-third of the sugar = 10%

CP of one-third of the sugar = Rs $\frac{4500}{3} = Rs . 1500$

$SP of one - third of the sugar = \frac{100 + gain %}{100} \times CP = Rs \frac{110}{100} \times 1500 = Rs 1650$

Now, profit= Rs (1650 − 1500) = Rs 150

At a profit of 12%, we have:
$SP of sugar = \frac{100 + gain %}{100} \times CP = Rs \frac{112}{100} \times 4500 = Rs 5040$

∴ Gain= Rs (5040 − 4500) = Rs 5400

Profit on the remaining amount of sugar = Rs (540 − 150) = Rs 390
CP of the remaining sugar = Rs (4500 − 1500) = Rs 3000

$Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{390}{3000} \times 100) % = 13 %$

Therefore, the profit on the remaining amount of sugar is 13%.

Answer:

Marked price = $Rs 4650$ and discount = 18%
Discount = 18% of marked price
$= 18 % o f R s 4650$
$= R s (4650 \times \frac{18}{100}) = R s 837$
Selling price = marked price − discount
$= Rs (4650 - 837) = Rs 3813$

Therefore, the selling price of the cooler is $Rs 3813$ .

Question 2:

Marked price = $Rs 4650$ and discount = 18%
Discount = 18% of marked price
$= 18 % o f R s 4650$
$= R s (4650 \times \frac{18}{100}) = R s 837$
Selling price = marked price − discount
$= Rs (4650 - 837) = Rs 3813$

Therefore, the selling price of the cooler is $Rs 3813$ .

Answer:

Marked Price = Rs 960
Selling Price = Rs 816
Discount = MP − SP
= Rs (960 − 816)
= Rs 144
$Rate of discount = 144 \times \frac{100}{960} = 15 %$

Therefore, the discount on the sweater is 15%.

Question 3:

Marked Price = Rs 960
Selling Price = Rs 816
Discount = MP − SP
= Rs (960 − 816)
= Rs 144
$Rate of discount = 144 \times \frac{100}{960} = 15 %$

Therefore, the discount on the sweater is 15%.

Answer:

SP of the shirt = â‚¹1,092
Discount = â‚¹208
MP = SP + Discount = â‚¹1,092 + â‚¹208 = â‚¹1,300
∴ Rate of discount = $\frac{Discount}{MP} \times 100 % = \frac{208}{1300} \times 100 % = 16 %$

Question 4:

SP of the shirt = â‚¹1,092
Discount = â‚¹208
MP = SP + Discount = â‚¹1,092 + â‚¹208 = â‚¹1,300
∴ Rate of discount = $\frac{Discount}{MP} \times 100 % = \frac{208}{1300} \times 100 % = 16 %$

Answer:

Selling Price = Rs 216.20
Rate of discount = 8%
Marked Price = ?
SP = MP − discount
Let the MP be Rs $x$ .

$Now, x - \frac{8}{100} \times x = 216.20 \Rightarrow \frac{92 x}{100} = 216.20 \Rightarrow 92 x = 21620 \Rightarrow x = \frac{21620}{92} \Rightarrow x = 235$

∴ Marked price = $R s 235$

Question 5:

Selling Price = Rs 216.20
Rate of discount = 8%
Marked Price = ?
SP = MP − discount
Let the MP be Rs $x$ .

$Now, x - \frac{8}{100} \times x = 216.20 \Rightarrow \frac{92 x}{100} = 216.20 \Rightarrow 92 x = 21620 \Rightarrow x = \frac{21620}{92} \Rightarrow x = 235$

∴ Marked price = $R s 235$

Answer:

Cost price = Rs 528
Rate of discount = 12%
Marked price = ?
SP= MP − discount
Let the MP be Rs $x$ .
$Now, \frac{x - 12}{100 \times x} = 528 \Rightarrow \frac{88 x}{100} = 528 \Rightarrow 88 x = 52800 \Rightarrow x = \frac{52800}{88} \Rightarrow x = Rs 600$

Therefore, the marked price of tea set is Rs 600.

Question 6:

Cost price = Rs 528
Rate of discount = 12%
Marked price = ?
SP= MP − discount
Let the MP be Rs $x$ .
$Now, \frac{x - 12}{100 \times x} = 528 \Rightarrow \frac{88 x}{100} = 528 \Rightarrow 88 x = 52800 \Rightarrow x = \frac{52800}{88} \Rightarrow x = Rs 600$

Therefore, the marked price of tea set is Rs 600.

Answer:

Let Rs 100 be the CP.
Then, marked price = $R s 135$
Discount = 20% of MP
    $= \frac{20}{100} \times 135 = 27$
Selling price = marked price − discount
   = 135 − 27
     = Rs 108
Now, gain = SP − CP
                  =108 − 100
                   =Rs 8

$∴ Gain percentage = \frac{gain}{CP} \times 100$

                            = $\frac{8}{100} \times 100 = 8 %$

Question 7:

Let Rs 100 be the CP.
Then, marked price = $R s 135$
Discount = 20% of MP
    $= \frac{20}{100} \times 135 = 27$
Selling price = marked price − discount
   = 135 − 27
     = Rs 108
Now, gain = SP − CP
                  =108 − 100
                   =Rs 8

$∴ Gain percentage = \frac{gain}{CP} \times 100$

                            = $\frac{8}{100} \times 100 = 8 %$

Answer:

Let Rs 100 be the CP.
Then, marked price = $R s 140$
Discount = 30% of MP
$= \frac{30}{100} \times 140 = 42$
Selling Price = marked price − discount
    = 140 − 42
= Rs 98
Now, loss = CP − SP
   = 100 − 98
           = Rs 2
$∴ L o s s p e r c e n t a g e = \frac{L o s s \times 100}{C P} = \frac{2 \times 100}{100} = 2 %$

Therefore, the shopkeeper had a loss of 2%.

Question 8:

Let Rs 100 be the CP.
Then, marked price = $R s 140$
Discount = 30% of MP
$= \frac{30}{100} \times 140 = 42$
Selling Price = marked price − discount
    = 140 − 42
= Rs 98
Now, loss = CP − SP
   = 100 − 98
           = Rs 2
$∴ L o s s p e r c e n t a g e = \frac{L o s s \times 100}{C P} = \frac{2 \times 100}{100} = 2 %$

Therefore, the shopkeeper had a loss of 2%.

Answer:

Cost price of the fan = $R s 1080$
Gain percentage = 25%
$∴ Selling price = \{\frac{(100 + gain %)}{100} \times CP\} = \{\frac{100 + 25}{100} \times 1080\} = \frac{125}{100} \times 1080 = Rs 1350$

Let the marked price be Rs $x$ .
Discount = 25% of $R s x$

$= \frac{25 x}{100}$

SP = MP − discount
⇒ 1350 = $X$ − $\frac{25 X}{100}$

$\Rightarrow 1350 = \frac{100 x - 25 x}{100} \Rightarrow 135000 = 75 x \Rightarrow x = \frac{13500}{75} \Rightarrow x = 1800$

Therefore, the marked price of the fan is $R s 1800$ .

Question 9:

Cost price of the fan = $R s 1080$
Gain percentage = 25%
$∴ Selling price = \{\frac{(100 + gain %)}{100} \times CP\} = \{\frac{100 + 25}{100} \times 1080\} = \frac{125}{100} \times 1080 = Rs 1350$

Let the marked price be Rs $x$ .
Discount = 25% of $R s x$

$= \frac{25 x}{100}$

SP = MP − discount
⇒ 1350 = $X$ − $\frac{25 X}{100}$

$\Rightarrow 1350 = \frac{100 x - 25 x}{100} \Rightarrow 135000 = 75 x \Rightarrow x = \frac{13500}{75} \Rightarrow x = 1800$

Therefore, the marked price of the fan is $R s 1800$ .

Answer:

Cost price of the refrigerator = $R s 11515$
Gain percentage = 20%.
$∴ Selling price = \{\frac{(100 + gain %)}{100} \times C . P\} = \{\frac{100 + 20}{100} \times 11515\} = \frac{120}{100} \times 11515 = Rs 13818$

Let the marked price be Rs $x$ .
Discount = 16% of $R s x$
$= \frac{16 x}{100}$
S.P = MP − Discount
⇒ 13818 = x − $\frac{16 x}{100}$

$\Rightarrow 13818 = \frac{100 x - 16 x}{100} \Rightarrow 1381800 = 84 x \Rightarrow x = \frac{1381800}{84} \Rightarrow x = 16450$

â€‹Therefore, the marked price of the refrigerator is $R s 16450$ .

Question 10:

Cost price of the refrigerator = $R s 11515$
Gain percentage = 20%.
$∴ Selling price = \{\frac{(100 + gain %)}{100} \times C . P\} = \{\frac{100 + 20}{100} \times 11515\} = \frac{120}{100} \times 11515 = Rs 13818$

Let the marked price be Rs $x$ .
Discount = 16% of $R s x$
$= \frac{16 x}{100}$
S.P = MP − Discount
⇒ 13818 = x − $\frac{16 x}{100}$

$\Rightarrow 13818 = \frac{100 x - 16 x}{100} \Rightarrow 1381800 = 84 x \Rightarrow x = \frac{1381800}{84} \Rightarrow x = 16450$

â€‹Therefore, the marked price of the refrigerator is $R s 16450$ .

Answer:

The cost price of the ring is $R s 1190$ .
Gain percentage = 20%.
$∴ Selling price = \{\frac{(100 + g a i n %)}{100} \times C . P\} = \{\frac{100 + 20}{100} \times 1190\} = \frac{120}{100} \times 1190 = Rs 1428$

Let the marked price be $x$ .
Discount = 16% of $R s x$
$= \frac{16 x}{100}$
SP = MP − Discount

$\Rightarrow 1428 = x - \frac{16 x}{100} \Rightarrow 1428 = \frac{100 x - 16 x}{100} \Rightarrow 142800 = 84 x \Rightarrow \frac{142800}{84} = x \Rightarrow x = 1700$

â€‹Therefore, the marked price of the ring is $Rs 1700$ .

Question 11:

The cost price of the ring is $R s 1190$ .
Gain percentage = 20%.
$∴ Selling price = \{\frac{(100 + g a i n %)}{100} \times C . P\} = \{\frac{100 + 20}{100} \times 1190\} = \frac{120}{100} \times 1190 = Rs 1428$

Let the marked price be $x$ .
Discount = 16% of $R s x$
$= \frac{16 x}{100}$
SP = MP − Discount

$\Rightarrow 1428 = x - \frac{16 x}{100} \Rightarrow 1428 = \frac{100 x - 16 x}{100} \Rightarrow 142800 = 84 x \Rightarrow \frac{142800}{84} = x \Rightarrow x = 1700$

â€‹Therefore, the marked price of the ring is $Rs 1700$ .

Answer:

Let $R s 100$ be the cost price.
Gain required = 17%
∴ Selling price = $R s 117$
Let the marked price be $R s x$ .
Then, discount = 10% of x
$= \frac{10}{100} \times x = \frac{x}{10}$
Selling Price = MP − discount
$\Rightarrow 117 = x - \frac{x}{10} \Rightarrow 117 = \frac{9 x}{10}$

$\Rightarrow 9 x = 1170 \Rightarrow x = \frac{1170}{9} \Rightarrow x = 130$

∴ Marked price = $R s 130$

Hence, the marked price is 30% above the cost price.

Question 12:

Let $R s 100$ be the cost price.
Gain required = 17%
∴ Selling price = $R s 117$
Let the marked price be $R s x$ .
Then, discount = 10% of x
$= \frac{10}{100} \times x = \frac{x}{10}$
Selling Price = MP − discount
$\Rightarrow 117 = x - \frac{x}{10} \Rightarrow 117 = \frac{9 x}{10}$

$\Rightarrow 9 x = 1170 \Rightarrow x = \frac{1170}{9} \Rightarrow x = 130$

∴ Marked price = $R s 130$

Hence, the marked price is 30% above the cost price.

Answer:

Let $R s 100$ be the cost price.
Gain required = 8%
Therefore, the selling price is $R s 108$ .
Let $R s x$ be the marked price.
Then, discount = 10% of x
$= \frac{10}{100} \times x = \frac{x}{10}$
Selling Price = MP − discount
$\Rightarrow 117 = x - \frac{x}{10} \Rightarrow 117 = \frac{9 x}{10}$

$\Rightarrow 9 x = 1080 \Rightarrow x = \frac{1080}{9} \Rightarrow x = 120$

∴ Marked price = $R s 120$

Hence, the marked price is 20% above the cost price.

Question 13:

Let $R s 100$ be the cost price.
Gain required = 8%
Therefore, the selling price is $R s 108$ .
Let $R s x$ be the marked price.
Then, discount = 10% of x
$= \frac{10}{100} \times x = \frac{x}{10}$
Selling Price = MP − discount
$\Rightarrow 117 = x - \frac{x}{10} \Rightarrow 117 = \frac{9 x}{10}$

$\Rightarrow 9 x = 1080 \Rightarrow x = \frac{1080}{9} \Rightarrow x = 120$

∴ Marked price = $R s 120$

Hence, the marked price is 20% above the cost price.

Answer:

Marked price of the TV = Rs 18500
First discount = 20%

$Now, 20 % o f 18500 = \frac{20}{100} \times 18500 = Rs 3700$

Price after the first discount = Rs (18500 − 3700)= Rs 14800
Second discount = 5% of 14800
$= \frac{5}{100} \times 14800 = 740$
Price after the second discount = (14800 − 740)
= Rs 14060
The TV is available for $Rs 14060 .$

Question 14:

Marked price of the TV = Rs 18500
First discount = 20%

$Now, 20 % o f 18500 = \frac{20}{100} \times 18500 = Rs 3700$

Price after the first discount = Rs (18500 − 3700)= Rs 14800
Second discount = 5% of 14800
$= \frac{5}{100} \times 14800 = 740$
Price after the second discount = (14800 − 740)
= Rs 14060
The TV is available for $Rs 14060 .$

Answer:

â€‹Let the marked price of the article be Rs 100.
First discount = 20%
Price after the first discount = (100 − 20) = Rs 80
Second discount = 5% of 80
$= \frac{5}{100} \times 80 = Rs 4$
Price after the second discount = (80 − 4) = Rs 76
Net selling price = Rs 76
∴ Single discount equivalent to the given successive discounts = (100 − 76)% = 24%

Question 1:

â€‹Let the marked price of the article be Rs 100.
First discount = 20%
Price after the first discount = (100 − 20) = Rs 80
Second discount = 5% of 80
$= \frac{5}{100} \times 80 = Rs 4$
Price after the second discount = (80 − 4) = Rs 76
Net selling price = Rs 76
∴ Single discount equivalent to the given successive discounts = (100 − 76)% = 24%

Answer:

List price of the refrigerator = Rs 14650
Sales tax = 6% of â€‹Rs 14650
$= Rs (14650 \times \frac{6}{100}) = Rs 879$

Bill amount $= Rs (14650 + 879)$
$= Rs 15529$
Hence, the cost of the refrigerator is Rs 15,529.

Question 2:

List price of the refrigerator = Rs 14650
Sales tax = 6% of â€‹Rs 14650
$= Rs (14650 \times \frac{6}{100}) = Rs 879$

Bill amount $= Rs (14650 + 879)$
$= Rs 15529$
Hence, the cost of the refrigerator is Rs 15,529.

Answer:

(i)
$Cost of the tie = Rs . 250$
$Sales tax = 6 % of Rs 250$
$= Rs . (250 \times \frac{6}{100}) = Rs . 15$
$Hence, bill amount = Rs (250 + 15)$
$= Rs . 265$

(ii) $Cost of the medicines = Rs . 625$
$Sales tax = 4 % of Rs . 625$
$= Rs . (625 \times \frac{4}{100}) = Rs . 25$
$Hence, bill amount = Rs (625 + 25)$
$= Rs 650$

$(iii) Cost of the cosmetics = Rs 430 Sales tax = 10 % of Rs 430$
$= Rs (430 \times \frac{10}{100}) = Rs 43$

$Hence, bill amount = Rs (430 + 43)$
$= Rs . 473$

$(iv) Cost of clothes = Rs 1175 Sales tax = 8 % of Rs 1175$
$= Rs (1175 \times \frac{8}{100}) = Rs 94$
$Hence, bill amount = Rs (1175 + 94)$
$= Rs . 1269$
$Therefore, total amount to be paid by Reena = bill amount of all the four items$
$= Rs (265 + 650 + 473 + 1269) = Rs 2657$

Question 3:

(i)
$Cost of the tie = Rs . 250$
$Sales tax = 6 % of Rs 250$
$= Rs . (250 \times \frac{6}{100}) = Rs . 15$
$Hence, bill amount = Rs (250 + 15)$
$= Rs . 265$

(ii) $Cost of the medicines = Rs . 625$
$Sales tax = 4 % of Rs . 625$
$= Rs . (625 \times \frac{4}{100}) = Rs . 25$
$Hence, bill amount = Rs (625 + 25)$
$= Rs 650$

$(iii) Cost of the cosmetics = Rs 430 Sales tax = 10 % of Rs 430$
$= Rs (430 \times \frac{10}{100}) = Rs 43$

$Hence, bill amount = Rs (430 + 43)$
$= Rs . 473$

$(iv) Cost of clothes = Rs 1175 Sales tax = 8 % of Rs 1175$
$= Rs (1175 \times \frac{8}{100}) = Rs 94$
$Hence, bill amount = Rs (1175 + 94)$
$= Rs . 1269$
$Therefore, total amount to be paid by Reena = bill amount of all the four items$
$= Rs (265 + 650 + 473 + 1269) = Rs 2657$

Answer:

Let the original price of the watch be Rs x.
VAT = 10% of Rs x
$= Rs (x \times \frac{10}{100}) = Rs \frac{10 x}{100}$
∴ Price including VAT = $Rs (x + \frac{x}{10})$
$= Rs \frac{11 x}{10}$
Now, $\frac{11 x}{10} = 1980$
$\Rightarrow x = (1980 \times \frac{10}{11}) = 1800$

Hence, the original price of the watch is Rs 1,800.

Question 4:

Let the original price of the watch be Rs x.
VAT = 10% of Rs x
$= Rs (x \times \frac{10}{100}) = Rs \frac{10 x}{100}$
∴ Price including VAT = $Rs (x + \frac{x}{10})$
$= Rs \frac{11 x}{10}$
Now, $\frac{11 x}{10} = 1980$
$\Rightarrow x = (1980 \times \frac{10}{11}) = 1800$

Hence, the original price of the watch is Rs 1,800.

Answer:

â€‹â€‹Let the original price of the shirt be Rs x.
VAT = 7% of Rs x
$= Rs . (x \times \frac{7}{100}) = Rs . \frac{7 x}{100}$
∴ Price including VAT = $Rs . (x + \frac{7 x}{100})$
$= Rs . \frac{107 x}{100}$
Now, $\frac{107 x}{100} = 1337.50$
$\Rightarrow x = Rs (1337.50 \times \frac{100}{107}) = Rs 1250$

Hence, the original price of the shirt is Rs 1,250.

Question 5:

â€‹â€‹Let the original price of the shirt be Rs x.
VAT = 7% of Rs x
$= Rs . (x \times \frac{7}{100}) = Rs . \frac{7 x}{100}$
∴ Price including VAT = $Rs . (x + \frac{7 x}{100})$
$= Rs . \frac{107 x}{100}$
Now, $\frac{107 x}{100} = 1337.50$
$\Rightarrow x = Rs (1337.50 \times \frac{100}{107}) = Rs 1250$

Hence, the original price of the shirt is Rs 1,250.

Answer:

Let the price of 10 g of gold be Rs x.
$VAT = 1 % of Rs x = Rs (x \times \frac{1}{100}) = Rs \frac{x}{100}$
∴ Price including VAT $= Rs . (x + \frac{x}{100})$
$= Rs \frac{101 x}{100}$
$Now, \frac{101 x}{100} = 15756 \Rightarrow x = Rs (15756 \times \frac{100}{101}) = Rs 15600$

Hence, the price of 10 g of gold is Rs 15,600.

Question 6:

Let the price of 10 g of gold be Rs x.
$VAT = 1 % of Rs x = Rs (x \times \frac{1}{100}) = Rs \frac{x}{100}$
∴ Price including VAT $= Rs . (x + \frac{x}{100})$
$= Rs \frac{101 x}{100}$
$Now, \frac{101 x}{100} = 15756 \Rightarrow x = Rs (15756 \times \frac{100}{101}) = Rs 15600$

Hence, the price of 10 g of gold is Rs 15,600.

Answer:

Let the original price of the computer be Rs x.
$VAT = 4 % of Rs . x = Rs . (x \times \frac{4}{100}) = Rs . \frac{4 x}{100}$
∴ Price including VAT $= Rs . (x + \frac{4 x}{100})$
$= Rs . \frac{104 x}{100}$
$Now, \frac{104 x}{100} = 37960 \Rightarrow x = (37960 \times \frac{100}{104}) = 36500$

∴ The original price of the computer is Rs 36,500

Question 7:

Let the original price of the computer be Rs x.
$VAT = 4 % of Rs . x = Rs . (x \times \frac{4}{100}) = Rs . \frac{4 x}{100}$
∴ Price including VAT $= Rs . (x + \frac{4 x}{100})$
$= Rs . \frac{104 x}{100}$
$Now, \frac{104 x}{100} = 37960 \Rightarrow x = (37960 \times \frac{100}{104}) = 36500$

∴ The original price of the computer is Rs 36,500

Answer:

â€‹Let the original cost of the spare parts be Rs x.
$VAT = 12 % of Rs . x = Rs . (x \times \frac{12}{100}) = Rs . \frac{12 x}{100}$
∴ Price including VAT $= Rs . (x + \frac{12 x}{100})$
$= Rs . \frac{112 x}{100}$
$Now, \frac{112 x}{100} = 20776 \Rightarrow x = (20776 \times \frac{100}{112}) = 18550$

Hence, â€‹the original cost of the spare parts is Rs 18,550.

Question 8:

â€‹Let the original cost of the spare parts be Rs x.
$VAT = 12 % of Rs . x = Rs . (x \times \frac{12}{100}) = Rs . \frac{12 x}{100}$
∴ Price including VAT $= Rs . (x + \frac{12 x}{100})$
$= Rs . \frac{112 x}{100}$
$Now, \frac{112 x}{100} = 20776 \Rightarrow x = (20776 \times \frac{100}{112}) = 18550$

Hence, â€‹the original cost of the spare parts is Rs 18,550.

Answer:

â€‹Let the list price of the TV set be Rs x.
$VAT = 8 % of Rs . x = Rs . (x \times \frac{8}{100}) = Rs . \frac{8 x}{100}$
∴ Price including VAT $= Rs . (x + \frac{8 x}{100})$
$= Rs . \frac{108 x}{100}$
$Now, \frac{108 x}{100} = 27000 \Rightarrow x = (27000 \times \frac{100}{108}) = 25000$

Hence, the list price of the TV set is Rs 25,000.

Question 9:

â€‹Let the list price of the TV set be Rs x.
$VAT = 8 % of Rs . x = Rs . (x \times \frac{8}{100}) = Rs . \frac{8 x}{100}$
∴ Price including VAT $= Rs . (x + \frac{8 x}{100})$
$= Rs . \frac{108 x}{100}$
$Now, \frac{108 x}{100} = 27000 \Rightarrow x = (27000 \times \frac{100}{108}) = 25000$

Hence, the list price of the TV set is Rs 25,000.

Answer:

Let the rate of VAT be x%. Then, we have:

$840 + x % o f 840 = 882 \Rightarrow (\frac{x}{100} \times 840) = 882 - 840 \Rightarrow \frac{84 x}{10} = 42 \Rightarrow x = (42 \times \frac{10}{84}) = 5$

∴ The rate of VAT is 5%.

Question 10:

Let the rate of VAT be x%. Then, we have:

$840 + x % o f 840 = 882 \Rightarrow (\frac{x}{100} \times 840) = 882 - 840 \Rightarrow \frac{84 x}{10} = 42 \Rightarrow x = (42 \times \frac{10}{84}) = 5$

∴ The rate of VAT is 5%.

Answer:

Let the rate of VAT be x%. Then, we have:

$18500 + x % o f 18500 = 19980 \Rightarrow (\frac{x}{100} \times 18500) = 19980 - 18500 \Rightarrow 185 x = 1480 \Rightarrow x = \frac{1480}{185} = 8$

∴ The rate of VAT is 8%.

Question 11:

Let the rate of VAT be x%. Then, we have:

$18500 + x % o f 18500 = 19980 \Rightarrow (\frac{x}{100} \times 18500) = 19980 - 18500 \Rightarrow 185 x = 1480 \Rightarrow x = \frac{1480}{185} = 8$

∴ The rate of VAT is 8%.

Answer:

Let the rate of VAT be x%. Then, we have:

$34000 + x % o f 34000 = 382500 \Rightarrow (\frac{x}{100} \times 340000) = 382500 - 340000 \Rightarrow 3400 x = 42500 \Rightarrow x = \frac{42500}{3400} = 12.5$

∴ The rate of VAT is 12.5%.

Question 1:

Let the rate of VAT be x%. Then, we have:

$34000 + x % o f 34000 = 382500 \Rightarrow (\frac{x}{100} \times 340000) = 382500 - 340000 \Rightarrow 3400 x = 42500 \Rightarrow x = \frac{42500}{3400} = 12.5$

∴ The rate of VAT is 12.5%.

Answer:

$(c) 33 \frac{1}{3} % SP = Rs 100 Gain = Rs (100 - 75) = Rs 25 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{25}{75} \times 100) % = 33 \frac{1}{3} %$

Question 2:

$(c) 33 \frac{1}{3} % SP = Rs 100 Gain = Rs (100 - 75) = Rs 25 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{25}{75} \times 100) % = 33 \frac{1}{3} %$

Answer:

$(b) 12 \frac{1}{2} % CP = Rs 120 SP = Rs 105 Loss = Rs (120 - 105) = Rs 15 ∴ Loss percentage = (\frac{loss}{CP} \times 100) = (\frac{15}{120} \times 100) = 12 \frac{1}{2} %$

Question 3:

$(b) 12 \frac{1}{2} % CP = Rs 120 SP = Rs 105 Loss = Rs (120 - 105) = Rs 15 ∴ Loss percentage = (\frac{loss}{CP} \times 100) = (\frac{15}{120} \times 100) = 12 \frac{1}{2} %$

Answer:

$(b) 25 % CP = SP - Gain = Rs (100 - 20) = Rs 80 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Question 4:

$(b) 25 % CP = SP - Gain = Rs (100 - 20) = Rs 80 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Answer:

$(d) Rs 72 SP = Rs 48 Loss = 20 % Now, CP = \frac{100}{100 - loss %} \times SP = Rs (\frac{100}{(100 - loss %)} \times SP) = Rs (\frac{100}{(100 - 20)} \times 48) = Rs (\frac{100}{80} \times 48) = Rs 60$

$∴ Desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$

$= \{\frac{(100 + 20)}{100} \times 60\} = Rs (\frac{12}{10} \times 60) = Rs 72$

Question 5:

$(d) Rs 72 SP = Rs 48 Loss = 20 % Now, CP = \frac{100}{100 - loss %} \times SP = Rs (\frac{100}{(100 - loss %)} \times SP) = Rs (\frac{100}{(100 - 20)} \times 48) = Rs (\frac{100}{80} \times 48) = Rs 60$

$∴ Desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$

$= \{\frac{(100 + 20)}{100} \times 60\} = Rs (\frac{12}{10} \times 60) = Rs 72$

Answer:

(c) 120%

Let the SP and CP of the article be Rs x and y, respectively.
Gain percentage = 10%
⇒ 10 = $\frac{x - y}{y} \times 100$
⇒ y = $\frac{10 x}{11}$

According to the question, we have:

SP = Rs 2x
∴ Gain percentage = $\frac{gain}{CP} \times 100$

$= \frac{2 x - \frac{10 x}{11}}{\frac{10 x}{11}} \times 100 = \frac{12}{10} \times 100 = 120 %$

Question 6:

(c) 120%

Let the SP and CP of the article be Rs x and y, respectively.
Gain percentage = 10%
⇒ 10 = $\frac{x - y}{y} \times 100$
⇒ y = $\frac{10 x}{11}$

According to the question, we have:

SP = Rs 2x
∴ Gain percentage = $\frac{gain}{CP} \times 100$

$= \frac{2 x - \frac{10 x}{11}}{\frac{10 x}{11}} \times 100 = \frac{12}{10} \times 100 = 120 %$

Answer:

(d) 125%
$Cost price of a banana = Rs \frac{2}{3} Selling price of a banana = Rs \frac{3}{2} Now, profit = Rs (\frac{3}{2} - \frac{2}{3}) = Rs \frac{9 - 4}{6} = Rs \frac{5}{6} ∴ Gain percentage = \frac{gain}{CP} \times 100 = \frac{(\frac{5}{6})}{(\frac{2}{3})} \times 100 = \frac{5}{6} \times \frac{3}{2} \times 100 = \frac{5}{4} \times 100 = 5 \times 25 = 125 %$

Question 7:

(d) 125%
$Cost price of a banana = Rs \frac{2}{3} Selling price of a banana = Rs \frac{3}{2} Now, profit = Rs (\frac{3}{2} - \frac{2}{3}) = Rs \frac{9 - 4}{6} = Rs \frac{5}{6} ∴ Gain percentage = \frac{gain}{CP} \times 100 = \frac{(\frac{5}{6})}{(\frac{2}{3})} \times 100 = \frac{5}{6} \times \frac{3}{2} \times 100 = \frac{5}{4} \times 100 = 5 \times 25 = 125 %$

Answer:

(c) 20%

$Let Rs x be the SP of each pen . SP of 10 pens = CP of 12 pens = Rs 12 x CP of 10 pens = Rs 10 x Now, gain = Rs (12 x - 10 x) = Rs 2 x ∴ Gain percentage = (\frac{gain}{CP} \times 100) %$
$= (\frac{2 x}{10 x} \times 100) % = 20 %$

Question 8:

(c) 20%

$Let Rs x be the SP of each pen . SP of 10 pens = CP of 12 pens = Rs 12 x CP of 10 pens = Rs 10 x Now, gain = Rs (12 x - 10 x) = Rs 2 x ∴ Gain percentage = (\frac{gain}{CP} \times 100) %$
$= (\frac{2 x}{10 x} \times 100) % = 20 %$

Answer:

(b) 25%

$Let the SP of 100 pens be Rs x . SP of 1 pen = Rs \frac{x}{100} Profit = Rs \frac{20 x}{100} = Rs \frac{x}{5} Now, CP = x - \frac{x}{5} = \frac{4 x}{5} ∴ Gain percentage = \frac{\frac{x}{5}}{\frac{4 x}{5}} \times 100 = 25 %$

Question 9:

(b) 25%

$Let the SP of 100 pens be Rs x . SP of 1 pen = Rs \frac{x}{100} Profit = Rs \frac{20 x}{100} = Rs \frac{x}{5} Now, CP = x - \frac{x}{5} = \frac{4 x}{5} ∴ Gain percentage = \frac{\frac{x}{5}}{\frac{4 x}{5}} \times 100 = 25 %$

Answer:

(d) 150%

â€‹ $L . C . M of 5 and 2 = (5 \times 1 \times 2) = 10 Let 10 be the number of toffees bought . CP of 5 toffees = Rs 1 CP of 1 toffee = Rs (\frac{1}{5}) ∴ CP of 10 toffees = Rs (\frac{1}{5} \times 10) = Rs 2 SP of 2 toffees = Rs 1 SP of 1 toffee = Rs (\frac{1}{2}) ∴ SP of 10 toffees = Rs (\frac{1}{2} \times 10)$
$= R s . 5$
$Gain = Rs (5 - 2) = Rs 3 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{3}{2} \times 100) % = 150 %$

Question 10:

(d) 150%

â€‹ $L . C . M of 5 and 2 = (5 \times 1 \times 2) = 10 Let 10 be the number of toffees bought . CP of 5 toffees = Rs 1 CP of 1 toffee = Rs (\frac{1}{5}) ∴ CP of 10 toffees = Rs (\frac{1}{5} \times 10) = Rs 2 SP of 2 toffees = Rs 1 SP of 1 toffee = Rs (\frac{1}{2}) ∴ SP of 10 toffees = Rs (\frac{1}{2} \times 10)$
$= R s . 5$
$Gain = Rs (5 - 2) = Rs 3 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{3}{2} \times 100) % = 150 %$

Answer:

(d) 25%

â€‹ $L . C . M of 5 and 6 = (5 \times 1 \times 6) = 30 Let 30 be the number of oranges bought . CP of 5 oranges = Rs 10 CP of 1 oranges = Rs (\frac{10}{5}) = Rs 2 ∴ CP of 30 oranges = Rs (2 \times 30) = Rs 60 SP of 6 oranges = Rs 15 SP of 1 oranges = Rs (\frac{15}{6}) ∴ SP of 30 oranges = Rs (\frac{15}{6} \times 30)$

$= Rs 75$

$Now, gain = Rs (75 - 60) = Rs 15 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{15}{60} \times 100) % = 25 %$

Question 11:

(d) 25%

â€‹ $L . C . M of 5 and 6 = (5 \times 1 \times 6) = 30 Let 30 be the number of oranges bought . CP of 5 oranges = Rs 10 CP of 1 oranges = Rs (\frac{10}{5}) = Rs 2 ∴ CP of 30 oranges = Rs (2 \times 30) = Rs 60 SP of 6 oranges = Rs 15 SP of 1 oranges = Rs (\frac{15}{6}) ∴ SP of 30 oranges = Rs (\frac{15}{6} \times 30)$

$= Rs 75$

$Now, gain = Rs (75 - 60) = Rs 15 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{15}{60} \times 100) % = 25 %$

Answer:

â€‹(a) 4%

$SP of the radio = Rs 950 Loss = 5 % CP = \{\frac{100}{(100 - loss)} \times SP\} = Rs \{\frac{100}{(100 - 5)} \times 950\} = Rs (\frac{100}{95} \times 950) = Rs 1000$

$Now, gain = Rs (1040 - 1000) = Rs 40 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{40}{1000} \times 100) % = 4 %$

Question 12:

â€‹(a) 4%

$SP of the radio = Rs 950 Loss = 5 % CP = \{\frac{100}{(100 - loss)} \times SP\} = Rs \{\frac{100}{(100 - 5)} \times 950\} = Rs (\frac{100}{95} \times 950) = Rs 1000$

$Now, gain = Rs (1040 - 1000) = Rs 40 ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{40}{1000} \times 100) % = 4 %$

Answer:

(a) 20%

$Let Rs x be the CP of each article . SP of an article = Rs \frac{6}{5} x Now, gain = (SP - CP) = Rs (\frac{6}{5} x - x) = Rs \frac{x}{5} ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{\frac{x}{5}}{x} \times 100) % = ((\frac{x}{5} \times \frac{1}{x}) \times 100) % = 20 %$

Question 13:

(a) 20%

$Let Rs x be the CP of each article . SP of an article = Rs \frac{6}{5} x Now, gain = (SP - CP) = Rs (\frac{6}{5} x - x) = Rs \frac{x}{5} ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{\frac{x}{5}}{x} \times 100) % = ((\frac{x}{5} \times \frac{1}{x}) \times 100) % = 20 %$

Answer:

â€‹ (b) Rs.1200

$SP = Rs 720 Loss percentage = 25 % CP = \{\frac{100}{(100 - loss %)} \times SP\} = Rs \{\frac{100}{(100 - 25)} \times SP\} = Rs (\frac{100}{85} \times 720) = Rs 960 ∴ Desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$
$= Rs . \{\frac{(100 + 25)}{100} \times 960\} = Rs . (\frac{125}{100} \times 960) = Rs . 1200$

Question 14:

â€‹ (b) Rs.1200

$SP = Rs 720 Loss percentage = 25 % CP = \{\frac{100}{(100 - loss %)} \times SP\} = Rs \{\frac{100}{(100 - 25)} \times SP\} = Rs (\frac{100}{85} \times 720) = Rs 960 ∴ Desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$
$= Rs . \{\frac{(100 + 25)}{100} \times 960\} = Rs . (\frac{125}{100} \times 960) = Rs . 1200$

Answer:

(a) 5%
â€‹

$CP = Rs . 20 x SP = Rs . 21 x Gain = Rs . (21 - 20) = Rs . x ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{x}{20 x} \times 100) % = 5 %$

Question 15:

(a) 5%
â€‹

$CP = Rs . 20 x SP = Rs . 21 x Gain = Rs . (21 - 20) = Rs . x ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{x}{20 x} \times 100) % = 5 %$

Answer:

(a) 1.5% gain

â€‹    $SP of the first chair = Rs 500 Gain percentage = 20 % ∴ CP of the first chair = \{\frac{100}{(100 + gain %)} \times SP\}$
   $= Rs . \{\frac{100}{(100 + 20)} \times 500\} = Rs . (\frac{100}{120} \times 500) = Rs . 416.67$

$SP of the second chair = Rs . 500 Loss percentage = 12 % ∴ CP of the second chair = \{\frac{100}{(100 - loss %)} \times SP\}$
$= Rs . \{\frac{100}{(100 - 12)} \times 500\} = Rs . (\frac{100}{88} \times 500) = Rs . 568.18$

   $Total CP of the two chairs = Rs . (416.67 + 568.18)$
$= R s . 984.85$
$T o t a l S P o f t h e t w o c h a i r s = R s . (500 \times 2)$
   $= R s . 1000$
   $S i n c e S P > C P, t h e r e i s a g a i n i n t h e w h o l e t r a n s a c t i o n . N o w, g a i n = R s . (1000 - 984.85) = R s . 15.15 ∴ G a i n p e r c e n t a g e = (\frac{g a i n}{C P} \times 100) % = (\frac{15.15}{984.85} \times 100) % = 1.5 %$

Question 16:

(a) 1.5% gain

â€‹    $SP of the first chair = Rs 500 Gain percentage = 20 % ∴ CP of the first chair = \{\frac{100}{(100 + gain %)} \times SP\}$
   $= Rs . \{\frac{100}{(100 + 20)} \times 500\} = Rs . (\frac{100}{120} \times 500) = Rs . 416.67$

$SP of the second chair = Rs . 500 Loss percentage = 12 % ∴ CP of the second chair = \{\frac{100}{(100 - loss %)} \times SP\}$
$= Rs . \{\frac{100}{(100 - 12)} \times 500\} = Rs . (\frac{100}{88} \times 500) = Rs . 568.18$

   $Total CP of the two chairs = Rs . (416.67 + 568.18)$
$= R s . 984.85$
$T o t a l S P o f t h e t w o c h a i r s = R s . (500 \times 2)$
   $= R s . 1000$
   $S i n c e S P > C P, t h e r e i s a g a i n i n t h e w h o l e t r a n s a c t i o n . N o w, g a i n = R s . (1000 - 984.85) = R s . 15.15 ∴ G a i n p e r c e n t a g e = (\frac{g a i n}{C P} \times 100) % = (\frac{15.15}{984.85} \times 100) % = 1.5 %$

Answer:

(b) Rs 530

$Let the CP be Rs x . Then, we have : 625 - x = x - 435 \Rightarrow x + x = 625 + 435 \Rightarrow 2 x = 1060 ∴ x = Rs 530$

Question 17:

(b) Rs 530

$Let the CP be Rs x . Then, we have : 625 - x = x - 435 \Rightarrow x + x = 625 + 435 \Rightarrow 2 x = 1060 ∴ x = Rs 530$

Answer:

â€‹(c) Rs 198

$CP = Rs 150 Total CP = Rs (150 + 10 % of 150) = Rs (150 + (\frac{10}{100} \times 150)) = Rs (150 + 15) = Rs 165 ∴ Desired SP = \{\frac{(100 + gain %)}{100} \times total CP\}$
$= Rs . \{\frac{(100 + 20)}{100} \times 165\} = Rs . (\frac{120}{100} \times 165) = Rs . 198$

Question 18:

â€‹(c) Rs 198

$CP = Rs 150 Total CP = Rs (150 + 10 % of 150) = Rs (150 + (\frac{10}{100} \times 150)) = Rs (150 + 15) = Rs 165 ∴ Desired SP = \{\frac{(100 + gain %)}{100} \times total CP\}$
$= Rs . \{\frac{(100 + 20)}{100} \times 165\} = Rs . (\frac{120}{100} \times 165) = Rs . 198$

Answer:

(a)â€‹ Rs. 50

$Let the CP be Rs x . Then, we have : (105 % of x) - (95 % of x) = 5 \Rightarrow (\frac{105}{100} \times x) - (\frac{95}{100} \times x) = 5 \Rightarrow (\frac{105 x}{100} - \frac{95 x}{100}) = 5 \Rightarrow \frac{(105 x - 95 x)}{100} = 5 \Rightarrow \frac{10 x}{100} = 5 \Rightarrow \frac{x}{10} = 5 \Rightarrow x = 50 ∴ CP = Rs 50$

Question 19:

(a)â€‹ Rs. 50

$Let the CP be Rs x . Then, we have : (105 % of x) - (95 % of x) = 5 \Rightarrow (\frac{105}{100} \times x) - (\frac{95}{100} \times x) = 5 \Rightarrow (\frac{105 x}{100} - \frac{95 x}{100}) = 5 \Rightarrow \frac{(105 x - 95 x)}{100} = 5 \Rightarrow \frac{10 x}{100} = 5 \Rightarrow \frac{x}{10} = 5 \Rightarrow x = 50 ∴ CP = Rs 50$

Answer:

â€‹(b) 8%

$Let the CP be Rs 100 . Then, marked price = Rs 120 Discount = 10 % of MP$

$= (10 % of Rs 120) = Rs . (120 \times \frac{10}{100}) = Rs . 12$

$Now, SP = (MP) - (discount) = Rs (120 - 12) = Rs 108 Gain percentage = (108 - 100) % = 8 %$

Question 20:

â€‹(b) 8%

$Let the CP be Rs 100 . Then, marked price = Rs 120 Discount = 10 % of MP$

$= (10 % of Rs 120) = Rs . (120 \times \frac{10}{100}) = Rs . 12$

$Now, SP = (MP) - (discount) = Rs (120 - 12) = Rs 108 Gain percentage = (108 - 100) % = 8 %$

Answer:

â€‹(c) 1% loss

$Let the CP be Rs 100 . Then, marked price = Rs 110 Discount = 10 % of MP$

= (10 % of Rs . 110) = Rs . (110 \times \frac{10}{100}) = Rs . 11

N o w, S P = (M P) - (d i s c o u n t) = R s (110 - 11) = R s 99 ∴ L o s s p e r c e n t a g e = (100 - 99) % = 1 %

Question 21:

â€‹(c) 1% loss

$Let the CP be Rs 100 . Then, marked price = Rs 110 Discount = 10 % of MP$

= (10 % of Rs . 110) = Rs . (110 \times \frac{10}{100}) = Rs . 11

N o w, S P = (M P) - (d i s c o u n t) = R s (110 - 11) = R s 99 ∴ L o s s p e r c e n t a g e = (100 - 99) % = 1 %

Answer:

(c) Rs.750

$Let the basic price be x . VAT = 10 % of Rs x = Rs (x \times \frac{10}{100}) = Rs \frac{x}{10} ∴ Price including VAT = Rs (x + \frac{x}{10})$
$= R s . \frac{11 x}{10}$
$Now, \frac{11 x}{10} = 825$
$\Rightarrow x = (825 \times \frac{10}{11}) \Rightarrow x = 750$

∴ The basic price of the watch is Rs 750.

Question 1:

(c) Rs.750

$Let the basic price be x . VAT = 10 % of Rs x = Rs (x \times \frac{10}{100}) = Rs \frac{x}{10} ∴ Price including VAT = Rs (x + \frac{x}{10})$
$= R s . \frac{11 x}{10}$
$Now, \frac{11 x}{10} = 825$
$\Rightarrow x = (825 \times \frac{10}{11}) \Rightarrow x = 750$

∴ The basic price of the watch is Rs 750.

Answer:

$SP = Rs 322 Gain percentage = 15 % ∴ CP = \{\frac{100}{(100 + gain %)} \times SP\}$
$= Rs . \{\frac{100}{(100 + 15)} \times 322\} = Rs . (\frac{100}{115} \times 322) = Rs . 280$
$Now, desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$
$= Rs . \{\frac{(100 + 20)}{100} \times 280\} = Rs . (\frac{120}{100} \times 280) = Rs . 336$

∴ The desired selling price is Rs 336.

Question 2:

$SP = Rs 322 Gain percentage = 15 % ∴ CP = \{\frac{100}{(100 + gain %)} \times SP\}$
$= Rs . \{\frac{100}{(100 + 15)} \times 322\} = Rs . (\frac{100}{115} \times 322) = Rs . 280$
$Now, desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$
$= Rs . \{\frac{(100 + 20)}{100} \times 280\} = Rs . (\frac{120}{100} \times 280) = Rs . 336$

∴ The desired selling price is Rs 336.

Answer:

$Let the CP of each pen be Rs x . CP of 16 pens = Rs 16 x SP of 16 pens = CP of 12 pens = Rs 12 x i . e ., CP > SP Now, loss = CP - SP = (16 x - 12 x) = R s . 4 x ∴ Loss percentage = \frac{loss}{CP} \times 100 = \frac{4 x}{16 x} \times 100 = 25 %$

Question 3:

$Let the CP of each pen be Rs x . CP of 16 pens = Rs 16 x SP of 16 pens = CP of 12 pens = Rs 12 x i . e ., CP > SP Now, loss = CP - SP = (16 x - 12 x) = R s . 4 x ∴ Loss percentage = \frac{loss}{CP} \times 100 = \frac{4 x}{16 x} \times 100 = 25 %$

Answer:

â€‹ $Let the CP be Rs x . Then, we have : (12 % of x) - (8 % of x) = 30 \Rightarrow (x \times \frac{12}{100}) - (x \times \frac{8}{100}) = 30 \Rightarrow (\frac{12 x}{100} - \frac{8 x}{100}) = 30 \Rightarrow \frac{4 x}{100} = 30 \Rightarrow x = (30 \times \frac{100}{4}) = 750$
$∴ The cost price of the chair is Rs 750 .$

Question 4:

â€‹ $Let the CP be Rs x . Then, we have : (12 % of x) - (8 % of x) = 30 \Rightarrow (x \times \frac{12}{100}) - (x \times \frac{8}{100}) = 30 \Rightarrow (\frac{12 x}{100} - \frac{8 x}{100}) = 30 \Rightarrow \frac{4 x}{100} = 30 \Rightarrow x = (30 \times \frac{100}{4}) = 750$
$∴ The cost price of the chair is Rs 750 .$

Answer:

$Let the CP be Rs 100 . Then, marked price = Rs 130 Discount = 10 % of MP$

$= (10 % of Rs . 130) = Rs . (130 \times \frac{10}{100}) = Rs . 13$

$Now, SP = (MP) - (discount) = Rs . (130 - 13) = Rs . 117 ∴ Gain percentage = (117 - 100) % = 17 %$
$∴ The gain percentage of the trader is 17 % .$

Question 5:

$Let the CP be Rs 100 . Then, marked price = Rs 130 Discount = 10 % of MP$

$= (10 % of Rs . 130) = Rs . (130 \times \frac{10}{100}) = Rs . 13$

$Now, SP = (MP) - (discount) = Rs . (130 - 13) = Rs . 117 ∴ Gain percentage = (117 - 100) % = 17 %$
$∴ The gain percentage of the trader is 17 % .$

Answer:

$Let the marked price be Rs 100 . Then, first discount on it = Rs 20 Price after the first discount = Rs (100 - 20)$
$= R s . 80$
$Second discount on it = 10 % of Rs 80$
$= Rs (80 \times \frac{10}{100}) = Rs 8$

$Price after the second discount = Rs . (80 - 8)$
$= Rs . 72$
$Net selling price = Rs . 72 Single discount equivalent to given successive discounts = (100 - 72) %$
$= 28 %$
$∴ The single discount equivalent to given successive discounts is 28 % .$

Question 6:

$Let the marked price be Rs 100 . Then, first discount on it = Rs 20 Price after the first discount = Rs (100 - 20)$
$= R s . 80$
$Second discount on it = 10 % of Rs 80$
$= Rs (80 \times \frac{10}{100}) = Rs 8$

$Price after the second discount = Rs . (80 - 8)$
$= Rs . 72$
$Net selling price = Rs . 72 Single discount equivalent to given successive discounts = (100 - 72) %$
$= 28 %$
$∴ The single discount equivalent to given successive discounts is 28 % .$

Answer:

â€‹ $Let the original price be Rs x . VAT = 10 % of Rs x = Rs (x \times \frac{10}{100}) = Rs \frac{x}{10} ∴ Price including VAT = Rs (x + \frac{x}{10})$
$= Rs . \frac{11 x}{10}$
$∴ \frac{11 x}{10} = 1870$
$\Rightarrow x = (1870 \times \frac{10}{11}) \Rightarrow x = 1700$
$∴ The original price of the watch is Rs 1, 700 .$

Question 7:

â€‹ $Let the original price be Rs x . VAT = 10 % of Rs x = Rs (x \times \frac{10}{100}) = Rs \frac{x}{10} ∴ Price including VAT = Rs (x + \frac{x}{10})$
$= Rs . \frac{11 x}{10}$
$∴ \frac{11 x}{10} = 1870$
$\Rightarrow x = (1870 \times \frac{10}{11}) \Rightarrow x = 1700$
$∴ The original price of the watch is Rs 1, 700 .$

Answer:

(b) 25%
â€‹
$Let Rs x be the SP of 100 pen s . SP of 1 pen = Rs \frac{x}{100} Profit on 100 pen s = selling price of 20 pens = \frac{20}{100} \times x = \frac{x}{5} Now, CP = SP - Profit = x - \frac{x}{5} = \frac{4 x}{5} ∴ Profit percent on 100 pens = \frac{profit}{CP} \times 100 = \frac{\frac{x}{5}}{\frac{4 x}{5}} \times 100 = 25 %$

Question 8:

(b) 25%
â€‹
$Let Rs x be the SP of 100 pen s . SP of 1 pen = Rs \frac{x}{100} Profit on 100 pen s = selling price of 20 pens = \frac{20}{100} \times x = \frac{x}{5} Now, CP = SP - Profit = x - \frac{x}{5} = \frac{4 x}{5} ∴ Profit percent on 100 pens = \frac{profit}{CP} \times 100 = \frac{\frac{x}{5}}{\frac{4 x}{5}} \times 100 = 25 %$

Answer:

(d) 25%

$SP = Rs 100 Gain = Rs 20 CP = Rs (100 - 20) = Rs 80 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Question 9:

(d) 25%

$SP = Rs 100 Gain = Rs 20 CP = Rs (100 - 20) = Rs 80 Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Answer:

(b) 20%

â€‹ $Let x be the CP of the article . Then, SP of the article = \frac{6}{5} x Now, gain = (SP - CP) = (\frac{6}{5} x - x) = \frac{x}{5} ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{\frac{x}{5}}{x} \times 100) % = ((\frac{x}{5} \times \frac{1}{x}) \times 100) % = 20 %$

Question 10:

(b) 20%

â€‹ $Let x be the CP of the article . Then, SP of the article = \frac{6}{5} x Now, gain = (SP - CP) = (\frac{6}{5} x - x) = \frac{x}{5} ∴ Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{\frac{x}{5}}{x} \times 100) % = ((\frac{x}{5} \times \frac{1}{x}) \times 100) % = 20 %$

Answer:

(c) Rs.920

$SP = Rs 680 Loss percentage = 15 % Now, CP = \{\frac{100}{(100 - loss %)} \times SP\}$
    $= Rs . \{\frac{100}{(100 - 15)} \times 680\} = Rs . (\frac{100}{85} \times 680) = Rs . 800$
$∴ Desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$
      $= Rs \{\frac{(100 + 15)}{100} \times 800\} = Rs (\frac{115}{100} \times 800) = Rs 920$

Question 11:

(c) Rs.920

$SP = Rs 680 Loss percentage = 15 % Now, CP = \{\frac{100}{(100 - loss %)} \times SP\}$
    $= Rs . \{\frac{100}{(100 - 15)} \times 680\} = Rs . (\frac{100}{85} \times 680) = Rs . 800$
$∴ Desired SP = \{\frac{(100 + gain %)}{100} \times CP\}$
      $= Rs \{\frac{(100 + 15)}{100} \times 800\} = Rs (\frac{115}{100} \times 800) = Rs 920$

Answer:

â€‹(c) 8%

$Let the CP be Rs 100 . Then, marked price = Rs 120 Discount = 10 % of MP$

$= (10 % o f Rs . 120) = Rs . (120 \times \frac{10}{100}) = Rs . 12$

$Now, SP = (MP) - (discount) = Rs (120 - 12) = Rs 108 ∴ Gain percentage = (108 - 100) % = 8 %$

Question 12:

â€‹(c) 8%

$Let the CP be Rs 100 . Then, marked price = Rs 120 Discount = 10 % of MP$

$= (10 % o f Rs . 120) = Rs . (120 \times \frac{10}{100}) = Rs . 12$

$Now, SP = (MP) - (discount) = Rs (120 - 12) = Rs 108 ∴ Gain percentage = (108 - 100) % = 8 %$

Answer:

â€‹(c) Rs.750

$Let the original price be Rs x . VAT = 8 % of Rs x = Rs (x \times \frac{8}{100}) = Rs \frac{8 x}{100} ∴ Price including VAT = Rs (x + \frac{8 x}{100})$
$= R s . \frac{108 x}{100}$
$Now, \frac{108 x}{10} = 810$
$\Rightarrow x = (810 \times \frac{100}{108}) \Rightarrow x = 750$

Question 13:

â€‹(c) Rs.750

$Let the original price be Rs x . VAT = 8 % of Rs x = Rs (x \times \frac{8}{100}) = Rs \frac{8 x}{100} ∴ Price including VAT = Rs (x + \frac{8 x}{100})$
$= R s . \frac{108 x}{100}$
$Now, \frac{108 x}{10} = 810$
$\Rightarrow x = (810 \times \frac{100}{108}) \Rightarrow x = 750$

Answer:

â€‹(i) The discount is reckoned on the marked price.
(ii) Gain or loss is always reckoned on the cost price.
(iii) SP = (Marked price) − (Discount).
(iv) VAT is charged on the selling price of the article.

Question 14:

â€‹(i) The discount is reckoned on the marked price.
(ii) Gain or loss is always reckoned on the cost price.
(iii) SP = (Marked price) − (Discount).
(iv) VAT is charged on the selling price of the article.

Answer:

â€‹(i) False (F)

$SP = \{\frac{(100 - loss %)}{100} \times CP\}$

(ii) True (T)

(iii) False (F)
Gain is reckoned on the cost price.

(iv) True (T)

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