Rs Aggarwal 2017 for Class 8 Math Chapter 1 - Rational Numbers

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Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 1 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 8 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 134:

Question 1:

Find the gain or loss per cent when:
(i) CP = Rs 620 and SP = Rs 713
(ii) CP = Rs 675 and SP = Rs 630
(iii) CP = Rs 345 and SP = Rs 372.60
(iv) CP = Rs 80 and SP = Rs 76.80

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

Page No 134:

Question 2:

Find the selling price when:
(i) CP = Rs 1650 and gain% = 4%
(ii) CP = Rs 915 and gain% = $6 \frac{2}{3} %$
(iii) CP = Rs 875 and loss% = 12%
(iv) CP = Rs 645 and loss% = $13 \frac{1}{3} %$

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)

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

Page No 134:

Question 3:

Find the cost price when:
(i) SP = Rs 1596 and gain% = 12%
(ii) SP = Rs 2431 and loss% = $6 \frac{1}{2} %$
(iii) SP = Rs 657.60 and loss% = 4%
(iv) SP = Rs 34.40 and gain% = $7 \frac{1}{2} %$

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

Page No 134:

Question 4:

Manjit bought an iron safe for ₹ 12160 and paid ₹ 340 for its transportation. Then, he sold it for ₹ 12875. Find his gain per cent

Answer:

CP of the iron safe = ₹12,160
Money spent on transportation = ₹340
Total CP = ₹12,160 + ₹340 = ₹12,500
SP of the iron safe = ₹12,875
Profit = SP − CP = ₹12,875 − ₹12,500 = ₹375
∴ Profit% = $\frac{Profit}{CP} \times 100 %$ $= \frac{375}{12500} \times 100 % = 3 %$

Page No 134:

Question 5:

Robin purchased an old car for Rs 73500. He spent Rs 10300 on repairs and paid Rs 2600 for its insurance. Then he sold it to a mechanic for Rs 84240. What was his percentage gain or loss?

Answer:

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

Page No 134:

Question 6:

Hari bought 20 kg of rice at ₹ 36 per kg and 25 kg of rice at ₹ 32 per kg. He mixed the two varieties and sold the mixture at ₹ 38 per kg. Find his gain per cent in the whole transaction.

Answer:

Total cost of rice of 1st variety = ₹36/kg × 20 kg = ₹720
Total cost of rice of 2nd variety = ₹32/kg × 25 kg = ₹800
Total cost of the two rice varieties = ₹720 + ₹800 = ₹1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = ₹38/kg × 45 kg = ₹1,710
Gain = SP − CP = ₹1,710 − ₹1,520 = ₹190
Gain% = $\frac{Gain}{CP} \times 100 % = \frac{190}{1520} \times 100 % = 12 \frac{1}{2} %$

Page No 134:

Question 7:

Coffee costing Rs 250 per kg was mixed with chicory costing Rs 75 per kg in the ratio 5 : 2 for a certain blend. If the mixture was sold at Rs 230 per kg, find the gain or loss per cent.

Answer:

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

Page No 134:

Question 8:

If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.

Answer:

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

Page No 134:

Question 9:

The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss per cent.

Answer:

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

Page No 134:

Question 10:

By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain per cent.

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 ₹x.
∴ CP of 125 cassettes = ₹125x
CP of 130 cassettes = ₹130x
SP of 125 cassettes = CP of 130 cassettes                    [From (2)]
⇒ SP of 125 cassettes = ₹130x
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%.

Page No 134:

Question 11:

By selling 45 lemons, a vendor loses a sum equal to the selling price of 3 lemons. Find his loss per cent.

Answer:

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

Page No 134:

Question 12:

Oranges are bought at 6 for ₹ 20 and sold at 4 for ₹ 18. Find the gain or loss per cent.

Answer:

LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = ₹20
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 = ₹18
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 = ₹54 − ₹40 = ₹14
∴ Profit% = $\frac{Profit}{CP} \times 100 % = \frac{14}{40} \times 100 % = 35 %$

Page No 134:

Question 13:

A vendor purchased bananas at ₹ 40 per dozen and sold them at 10 for ₹ 36. Find his gain or loss per cent.

Answer:

LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = ₹40
∴ CP of 1 banana = $\frac{40}{12} = ₹ \frac{10}{3}$
⇒ CP of 60 bananas = $60 \times \frac{10}{3} = ₹ 200$
SP of 10 bananas = ₹36
∴ 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 = ₹216 − ₹200 = ₹16
∴ Profit% = $\frac{Profit}{CP} \times 100 % = \frac{16}{200} \times 100 = 8 %$

Page No 134:

Question 14:

A man bought apples at 10 for ₹ 75 and sold them at ₹ 75 per dozen. Find his loss per cent.

Answer:

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

Page No 134:

Question 15:

A man purchased some eggs at 3 for ₹ 16 and sold them at 5 for ₹ 36. Thus, he gained ₹ 168 in all. How many eggs did he purchase?

Answer:

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

Page No 135:

Question 16:

A dealer sold a camera for Rs 1080 gaining $\frac{1}{8}$ of its cost price. Find (i) the cost price of the camera, and (ii) the gain per cent earned by the dealer.

Answer:

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

Page No 135:

Question 17:

Meenakshi sells a pen for Rs 54 and loses $\frac{1}{10}$ of her outlay. Find (i) the cost price of the pen, and (ii) the loss per cent.

Answer:

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

Page No 135:

Question 18:

A dealer gets ₹ 940 more if instead of selling a table at a loss of 10%, it is sold at a gain of 10%. Find the cost price of the table.

Answer:

Let the cost price be ₹x.
Loss = 10% of ₹x = $\frac{10}{100} x = ₹ \frac{x}{10}$
SP in case of loss = CP − Loss = $x - \frac{x}{10} = ₹ \frac{9 x}{10}$
Gain =10% of ₹x = $\frac{10}{100} x = ₹ \frac{x}{10}$
SP in case of profit = CP + Profit = $x + \frac{x}{10} = ₹ \frac{11 x}{10}$
It is given that dealer gets ₹940 more if sold at a profit of 10% instead of loss of 10%.
∴ SP in case of profit − SP in case of loss = ₹940
$\Rightarrow \frac{11 x}{10} - \frac{9 x}{10} = 940 \Rightarrow \frac{2 x}{10} = 940 \Rightarrow x = 4700$
Hence, the cost price of the table is ₹4,700.

Page No 135:

Question 19:

A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair.

Answer:

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

Page No 135:

Question 20:

A cycle was sold at a gain of 10%. Had it been sold for ₹ 260 more, the gain would have been 14%. Find the cost price of the cycle.

Answer:

Let the CP be ₹x.
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% = ₹260
$∴ \frac{114 x}{100} - \frac{110 x}{100} = 260 \Rightarrow \frac{4 x}{100} = 260 \Rightarrow x = 6500$
Hence, the CP of the cycle is ₹6,500.

Page No 135:

Question 21:

Sonu buys 40 kg of wheat at ₹ 12.50 per kg and 30 kg of wheat at ₹ 14 per kg. At what rate per kg should he sell the mixture to gain 5% on the whole?

Answer:

40 kg of wheat is bought for ₹12.50/kg.
∴ CP of 40 kg of wheat = 40 × 12.50 = ₹500
30 kg of wheat is bought for ₹14/kg.
∴ CP of 30 kg of wheat = 30 × 14 = ₹420
Total CP = ₹500 + ₹420 = ₹920
Profit = 5% of CP = 5% of ₹920 = $\frac{5}{100} \times 920 = ₹ 46$
Let the SP be ₹x.
Profit = SP − CP
⇒ x − 920 = 46
⇒ x = ₹966
SP of 70 kg wheat = ₹966
∴ SP of 1 kg wheat = $\frac{966}{70} = ₹ 13.80$
Thus, the selling price of the mixture is ₹13.80/kg.

Page No 135:

Question 22:

Wasim bought two cricket bats for ₹ 840 and ₹ 360 respectively. He sells the first bat at a gain of 15% and the second one at a loss of 5%. Find his gain or loss per cent in the whole transaction.

Answer:

CP of the first bat = ₹840
Profit% on the first bat = 15%
∴ Profit = 15% of ₹840 = $\frac{15}{100} \times 840 = ₹ 126$
SP of the first bat = ₹840 + ₹126 = ₹966
CP of the second bat = ₹360
Loss = 5% of ₹360 = $\frac{5}{100} \times 360 = ₹ 18$
SP of the second bat = ₹360 − ₹18 = ₹342
Total CP of two bats = CP of first bat + CP of second bat = ₹840 + ₹360 = ₹1,200
Total SP of two bats = SP of first bat + SP of second bat = ₹966 + ₹342 = ₹1,308
Here, Total SP of two bats > Total CP of two bats.
Gain = Total SP of two bats − Total CP of two bats = ₹1,308 − ₹1,200 = ₹108
∴ Gain% in the whole transaction $= \frac{Gain}{Total CP of two bats} \times 100 %$ $= \frac{108}{1200} \times 100 = 9 %$

Page No 135:

Question 23:

Hema bought two pairs of jeans for ₹ 1450 each. She sold one of them at a gain of 8% and the other at a loss of 4%. Find her gain or loss per cent in the whole transaction.

Answer:

CP of first jeans = ₹1,450
Profit = 8% of CP = $\frac{8}{100} \times 1450 = ₹ 116$
SP of first jeans = ₹1,450 + ₹116 = ₹1,566
CP of second jeans = ₹1,450
Loss = 4% of CP = $\frac{4}{100} \times 1450 = ₹ 58$
SP of second jeans = ₹1450 − ₹58 = ₹1,392
Total CP of two jeans = CP of first jeans + CP of second jeans = ₹1,450 + ₹1,450 = ₹2,900
Total SP of two jeans = SP of first jeans + SP of second jeans = ₹1,566 + ₹1,392 = ₹2,958
Here, Total SP of two jeans > Total CP of two jeans.
Gain = Total SP of two jeans − Total CP of two jeans = ₹2,958 − ₹2,900 = ₹58
∴ Gain% = $\frac{Gain}{Total CP of two jeans} \times 100 % = \frac{58}{2900} \times 100 % = 2 %$

Page No 135:

Question 24:

A grocer purchased 200 kg of rice at Rs 25 per kg. He sold 80 kg of it at a gain of 10% and 40 kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total investment?

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

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

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

Page No 135:

Question 25:

If the selling price of a TV set is equal to $\frac{6}{5}$ of its cost price, find the gain per cent.

Answer:

Let the CP of the TV set be ₹x.
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% = $\frac{Gain}{CP} \times 100 % = \frac{\frac{x}{5}}{x} \times 100 % = \frac{100}{5} % = 20 %$

Page No 135:

Question 26:

If the selling price of a flower vase is $\frac{5}{6}$ of its cost price, find the loss per cent.

Answer:

Let the CP of the flower vase set be ₹x.
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% = $\frac{Loss}{CP} \times 100 % = \frac{\frac{x}{6}}{x} \times 100 % = \frac{100}{6} % = \frac{50}{3} % = 16 \frac{2}{3} %$

Page No 135:

Question 27:

By selling a bouquet for Rs 322, a florist gains 15%. At what price should he sell it to gain 25%?

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%

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

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

Page No 135:

Question 28:

By selling an umbrella for ₹ 336, a shopkeeper loses 4%. At what price must he sell it to gain 4%?

Answer:

Let the CP of the umbrella be ₹x.
SP of the umbrella = ₹336
Loss = 4% of ₹x = $₹ \frac{4}{100} x$
CP − Loss = SP
$\Rightarrow x - \frac{4}{100} x = 336 \Rightarrow \frac{96}{100} x = 336 \Rightarrow x = ₹ 350$
∴ CP of the umbrella = ₹350
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 ₹364.

Page No 135:

Question 29:

A radio is sold for Rs 3120 at a loss of 4%. What will be the gain or loss per cent if it is sold for Rs 3445?

Answer:

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

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%

Page No 135:

Question 30:

Luxmi sold two sarees for ₹ 1980 each. On one, she lost 10%, while on the other she gained 10%. Find her gain or loss per cent in the whole transaction.

Answer:

SP of first saree = ₹1,980
Loss = 10%
Let the CP of first saree be ₹x.
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 = ₹2,200
SP of second saree = ₹1,980
Gain = 10%
Let the CP of second saree be ₹y.
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 = ₹1,800
Total CP of two sarees = CP of first saree + CP of second saree = ₹2,200 + ₹1,800 = ₹4,000
Total SP of two sarees = SP of first saree + SP of second saree = ₹1,980 + ₹1,980 = ₹3,960
Here, Total CP of two sarees > Total SP of two sarees
Loss = Total CP of two sarees − Total SP of two sarees = ₹4,000 − ₹3,960 = ₹40
∴ Loss% in the whole transaction $= \frac{Loss}{Total CP of two sarees} \times 100 % = \frac{40}{4000} \times 100 % = 1 %$

Page No 135:

Question 31:

A shopkeeper sold two fans for ₹ 1140 each. On one he gains 14%, while on the other he loses 5%. Calculate his gain or loss per cent in the whole transaction.

Answer:

SP of first fan = ₹1,140
Gain = 14%
Let the CP of first fan be ₹x.
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 = ₹1,000
SP of second fan = ₹1,140
Loss = 5%
Let the CP of second fan be ₹y.
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 = ₹1,200
Total CP of two fans = CP of first fan + CP of second fan = ₹1,000 + ₹1,200 = ₹2,200
Total SP of two fans = SP of first fan + SP of second fan = ₹1,140 + ₹1,140 = ₹2,280
Here, Total SP of two fans > Total CP of two fans
Gain = Total SP of two fans − Total CP of two fans = ₹2,280 − ₹2,200 = ₹80
∴ Gain% on whole transaction $= \frac{Gain}{Total CP of two fans} \times 100 % = \frac{80}{2200} \times 100 % = 3.64 %$

Page No 135:

Question 32:

Vinod sold a watch to Arun at a gain of 12% and Arun had to sell it to Manoj at a loss of 5%. If manoj paid ₹ 3990 for it, how much did vinod pay for the watch?

Answer:

Let the CP of the watch for Vinod be ₹x.
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 = ₹3,990
So,
$\frac{112}{100} x (\frac{95}{100}) = 3990$
$\Rightarrow x = \frac{3990 \times 100 \times 100}{112 \times 95} = 3750$
Thus, Vinod paid ₹3,750 for the watch.

Page No 135:

Question 33:

Ahmed buys a plot of land for ₹ 480000. He sells of it at a loss of 6%. At what gain per cent should he sell the remaining part of the plot to gain 10% on the whole?

Answer:

CP of the plot of land = ₹4,80,000
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 = ₹2,88,000
Total gain% = 10%
Total gain = $\frac{10}{100} \times 480000 = ₹ 48, 000$
Total SP = CP + Gain = ₹4,80,000 + ₹48,000 = ₹5,28,000
SP of $\frac{3}{5}$ th of the land = ₹5,28,000 − ₹1,80,480 = ₹3,47,520
Gain on $\frac{3}{5}$ th of the land = SP of $\frac{3}{5}$ th land − CP of $\frac{3}{5}$ th land
= ₹3,47,520 − ₹2,88,000
= ₹59,520
Gain% on seling the remaining part of the plot = $\frac{Gain}{CP of \frac{3}{5} th land} \times 100 % = \frac{59520}{288000} \times 100 % = 20 \frac{2}{3} %$

Page No 135:

Question 34:

A grocer bought sugar worth Rs 4500. He sold one-third of it at a gain of 10%. At what gain per cent must the remaining sugar be sold to have a gain of 12% on the whole?

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%.

Page No 138:

Question 1:

The marked price of a water cooler is Rs 4650. The shopkeeper offers an off-season discount of 18% on it. Find its selling price.

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 $Rs 3813$ .

Page No 138:

Question 2:

The price of a sweater was slashed from Rs 960 to Rs 816 by a shopkeeper in the winter season. Find the rate of discount given by him.

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%.

Page No 138:

Question 3:

Find the rate of discount being given on a shirt whose selling price is ₹ 1092 after deducting a discount of ₹ 208 on its marked price.

Answer:

SP of the shirt = ₹1,092
Discount = ₹208
MP = SP + Discount = ₹1,092 + ₹208 = ₹1,300
∴ Rate of discount = $\frac{Discount}{MP} \times 100 % = \frac{208}{1300} \times 100 % = 16 %$

Page No 138:

Question 4:

After allowing a discount of 8% on a toy, it is sold for Rs 216.20. Find the marked price of the toy.

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 = $R s 235$

Page No 138:

Question 5:

A tea set was bought for Rs 528 after getting a discount of 12% on its marked price. Find the marked price of the tea set.

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.

Page No 138:

Question 6:

A dealer marks his goods at 35% above the cost price and allows a discount of 20% on the marked price. Find the gain or loss per cent.

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

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

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

Page No 138:

Question 7:

A cellphone was marked at 40% above the cost price and a discount of 30% was given on its marked price. Find the gain or loss per cent made by the shopkeeper.

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%.

Page No 138:

Question 8:

A dealer purchased a fan for Rs 1080. After allowing a discount of 25% on its marked price, he gains 25%. Find the marked price of the fan.

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 $R s 1800$ .

Page No 138:

Question 9:

A dealer bought a refrigerator for Rs 11515. After allowing a discount of 16% on its marked price, he gains 20%. Find the marked price of the refrigerator.

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 − $\frac{16 x}{100}$

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

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

Page No 138:

Question 10:

A jeweller allows a discount of 16% to his customers and still gains 20%. Find the marked price of a ring which costs the jeweller Rs 1190.

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

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

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

Page No 138:

Question 11:

After allowing a discount of 10% on the marked price, a trader still makes a gain of 17%. By what per cent is the marked price above the cost price?

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.

Page No 138:

Question 12:

How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 10% on the marked price, he gains 8%?

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.

Page No 138:

Question 13:

The marked price of a TV is Rs 18500. A dealer allows two successive discounts of 20% and 5%. For how much is the TV available?

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 $Rs 14060 .$

Page No 138:

Question 14:

Find the single discount which is equivalent to two successive discounts of 20% and 5%.

Answer:

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%

Page No 139:

Question 1:

The list price of a refrigerator is Rs 14650. If 6% is charged as sales tax, find the cost of the refrigerator.

Answer:

List price of the refrigerator = Rs 14650
Sales tax = 6% of 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.

Page No 139:

Question 2:

Reena bought the following articles from a general store:
(i) 1 tie costing Rs 250 with ST @ 6%
(ii) Medicines costing Rs 625 with ST @ 4%
(iii) Cosmetics costing Rs 430 with ST @ 10%
(iv) Clothes costing Rs 1175 with ST @ 8%
Calculate the total amount to be paid by Reena.

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

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

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

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

Page No 139:

Question 3:

Tanvy bought a watch for Rs 1980 including VAT at 10%. Find the original price of the watch.

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.

Page No 139:

Question 4:

Mohit bought a shirt for Rs 1337.50 including VAT at 7%. Find the original price of the shirt.

Answer:

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.

Page No 139:

Question 5:

Karuna bought 10 g of gold for Rs 15756 including VAT at 1%. What is the rate of gold per 10 g?

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.

Page No 139:

Question 6:

Mohini purchased a computer for Rs 37960 including VAT at 4%. What is the original price of the computer?

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

Page No 139:

Question 7:

Sajal purchased some car parts for Rs 20776 including VAT at 12%. What is the original cost of these spare parts?

Answer:

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, the original cost of the spare parts is Rs 18,550.

Page No 139:

Question 8:

The sale price of a TV set including VAT is Rs 27000. If the VAT is charged at 8% of the list price, what is the list price of the TV set?

Answer:

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.

Page No 139:

Question 9:

Rohit purchased a pair of shoes for Rs 882 inclusive of VAT. If the original cost be Rs 840, find the rate of VAT.

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%.

Page No 139:

Question 10:

Malti bought a VCR for Rs 19980 including VAT. If the original price of VCR be Rs 18500, find the rate of VAT.

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%.

Page No 139:

Question 11:

The value of a car including VAT is Rs 382500. If the basic price of the car be Rs 340000, find the rate of VAT on cars.

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%.

Page No 140:

Question 1:

Tick (✓) the correct answer:
Rajan buys a toy for Rs 75 and sells it for Rs 100. His gain per cent is
(a) 25%
(b) 20%
(c) $33 \frac{1}{3} %$
(d) $37 \frac{1}{2} %$

Answer:

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

Page No 140:

Question 2:

Tick (✓) the correct answer:
A bat is bought for Rs 120 and sold for Rs 105. The loss per cent is
(a) 15%
(b) $12 \frac{1}{2} %$
(c) $16 \frac{2}{3} %$
(d) $14 \frac{1}{5} %$

Answer:

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

Page No 140:

Question 3:

Tick (✓) the correct answer:
A bookseller sells a book for Rs 100, gaining Rs 20. His gain per cent is
(a) 20%
(b) 25%
(c) 22%
(d) none of these

Answer:

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

Page No 140:

Question 4:

On selling an article for Rs 48, a shopkeeper loses 20%. In order to gain 20%, what would be the selling price?
(a) Rs 52
(b) Rs 56
(c) Rs 68
(d) Rs 72

Answer:

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

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

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

Page No 140:

Question 5:

Tick (✓) the correct answer:
On selling an article at a certain price a man gains 10%. On selling the same article at double the price, gain per cent is
(a) 20%
(b) 100%
(c) 120%
(d) 140%

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 = $\frac{gain}{CP} \times 100$

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

Page No 140:

Question 6:

Tick (✓) the correct answer:
Bananas are bought at 3 for Rs 2 and sold at 2 for Rs 3. The gain per cent is
(a) 25%
(b) 50%
(c) 75%
(d) 125%

Answer:

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

Page No 140:

Question 7:

Tick (✓) the correct answer:
If the selling price of 10 pens is the same as the cost price of 12 pens then gain per cent is
(a) 2%
(b) 12%
(c) 20%
(d) 25%

Answer:

(c) 20%

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

Page No 140:

Question 8:

Tick (✓) the correct answer:
On selling 100 pencils a man gains the selling price of 20 pencils. His gain per cent is
(a) 20%
(b) 25%
(c) $22 \frac{1}{2} %$
(d) $16 \frac{2}{3} %$

Answer:

(b) 25%

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

Page No 140:

Question 9:

Tick (✓) the correct answer:
Ravi buys some toffees at 5 for a rupee and sells them at 2 for a rupee. His gain per cent is
(a) 30%
(b) 40%
(c) 50%
(d) 150%

Answer:

(d) 150%

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

Page No 140:

Question 10:

Tick (✓) the correct answer:
Oranges are bought at 5 for Rs 10 and sold at 6 for Rs 15. His gain per cent is
(a) 50%
(b) 40%
(c) 35%
(d) 25%

Answer:

(d) 25%

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

$= Rs 75$

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

Page No 140:

Question 11:

Tick (✓) the correct answer:
By selling a radio for Rs 950, a man loses 5%. What per cent shall he gain by selling it for Rs 1040?
(a) 4%
(b) 4.5%
(c) 5%
(d) 9%

Answer:

(a) 4%

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

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

Page No 140:

Question 12:

Tick (✓) the correct answer:
The selling price of an article is $\frac{6}{5}$ of the cost price. The gain per cent is
(a) 20%
(b) 25%
(c) 30%
(d) 120%

Answer:

(a) 20%

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

Page No 140:

Question 13:

Tick (✓) the correct answer:
On selling a chair for Rs 720, a man loses 25%. To gain 25% it must be sold for
(a) Rs 900
(b) Rs 1200
(c) Rs 1080
(d) Rs 1440

Answer:

(b) Rs.1200

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

Page No 140:

Question 14:

Tick (✓) the correct answer:
The ratio of cost price and selling price of an article is 20 : 21. What is the gain per cent on it?
(a) 5%
(b) $5 \frac{1}{2} %$
(c) 6%
(d) $6 \frac{1}{4} %$

Answer:

(a) 5%

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

Page No 140:

Question 15:

Tick (✓) the correct answer:
A man sold two chairs for Rs 500 each. On one he gains 20% and on the other he loses 12%. His net gain or loss per cent is
(a) 1.5% gain
(b) 2% gain
(c) 1.5% loss
(d) 2% loss

Answer:

(a) 1.5% gain

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

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

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

Page No 141:

Question 16:

Tick (✓) the correct answer:
The profit earned on selling an article for Rs 625 is the same as loss on selling it for Rs 435. The cost price of the article is
(a) Rs 520
(b) Rs 530
(c) Rs 540
(d) Rs 550

Answer:

(b) Rs 530

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

Page No 141:

Question 17:

Tick (✓) the correct answer:
A man buys an article for Rs 150 and makes overhead expenses which are 10% of the cost price. At what price must he sell it to gain 20%?
(a) Rs 182
(b) Rs 192
(c) Rs 198
(d) Rs 208

Answer:

(c) Rs 198

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

Page No 141:

Question 18:

Tick (✓) the correct answer:
If an article is sold at a gain of 5% instead of being sold at a loss of 5%, a man gets Rs 5 more. What is the cost price of the article?
(a) Rs 50
(b) Rs 40
(c) Rs 60
(d) Rs 80

Answer:

(a) Rs. 50

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

Page No 141:

Question 19:

Tick (✓) the correct answer:
A dealer lists his articles at 20% above cost price and allows a discount of 10%. His gain per cent is
(a) 10%
(b) 8%
(c) 9 %
(d) $8 \frac{1}{4} %$

Answer:

(b) 8%

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

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

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

Page No 141:

Question 20:

Tick (✓) the correct answer:
The marked price of an article is 10% more than the cost price and a discount of 10% is given on the marked price. The seller has
(a) no gain and no loss
(b) 1% gain
(c) 1% loss
(d) none of these

Answer:

(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 %

Page No 141:

Question 21:

Tick (✓) the correct answer:
The price of watch including 10% VAT is Rs 825. What is its basic price?
(a) Rs 742.52
(b) Rs 775
(c) Rs 750
(d) Rs 907.50

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.

Page No 142:

Question 1:

By selling a flower pot for Rs 322, a man gains 15%. At what price should he sell it to gain 20%?

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.

Page No 142:

Question 2:

If the cost price of 12 pens is equal to the selling price of 16 pens, find the loss per cent.

Answer:

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

Page No 142:

Question 3:

A dealer gets Rs 30 less if instead of selling a chair at a gain of 12% he sells it at a gain of 8%. Find the cost price of the chair.

Answer:

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

Page No 142:

Question 4:

A trader marks his goods at 30% above cost price and allows a discount of 10%. What is his gain per cent?

Answer:

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

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

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

Page No 142:

Question 5:

Find the single discount equivalent to two successive discounts of 20% and 10%.

Answer:

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

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

Page No 142:

Question 6:

Rajan bought a watch for Rs 1870 including VAT at 10%. Find the original price of the watch.

Answer:

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

Page No 142:

Question 7:

Mark (✓) against the correct answer:
On selling 100 pens, a man gains the selling price of 20 pens. The gain per cent is
(a) 20%
(b) 25%
(c) $16 \frac{2}{3} %$
(d) 15%

Answer:

(b) 25%

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

Page No 142:

Question 8:

Mark (✓) against the correct answer:
A man sells a bat for Rs 100 gaining Rs 20. His gain per cent is
(a) 20%
(b) 22%
(c) 18%
(d) 25%

Answer:

(d) 25%

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

Page No 142:

Question 9:

Mark (✓) against the correct answer:
The selling price of an article is $\frac{6}{5}$ of the cost price. The gain per cent is
(a) 15%
(b) 20%
(c) 25%
(d) 30%

Answer:

(b) 20%

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

Page No 142:

Question 10:

Mark (✓) against the correct answer:
On selling a chair for Rs 680, a man loses 15%. To gain 15%, it must be sold for
(a) Rs 800
(b) Rs 860
(c) Rs 920
(d) Rs 884

Answer:

(c) Rs.920

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

Page No 142:

Question 11:

Mark (✓) against the correct answer:
A dealer lists his goods at 20% above cost price and allows a discount of 10%. His gain per cent is
(a) 10%
(b) 9%
(c) 8%
(d) 12%

Answer:

(c) 8%

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

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

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

Page No 142:

Question 12:

Mark (✓) against the correct answer:
The price of a watch including 8% VAT is Rs 810. What is its basic price?
(a) Rs 675
(b) Rs 729
(c) Rs 750
(d) Rs 745

Answer:

(c) Rs.750

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

Page No 142:

Question 13:

Fill in the blanks.
(i) The discount is reckoned on the ......... price.
(ii) Gain or loss is always reckoned on the .........
(iii) SP = (Marked price) − (.........)
(iv) VAT is charged on the ......... of the article.

Answer:

(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.

Page No 142:

Question 14:

Write 'T' for true and 'F' for false for each of the following:
(i) SP = $\frac{(100 + loss %)}{100} \times CP .$
(ii) CP = $\frac{100}{(100 + gain %)} \times SP .$
(iii) Gain is reckoned on the selling price.
(iv) The discount is allowed on the marked price.

Answer:

(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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