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#### 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

(ii)

(iii)

(iv)

#### 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% = $13\frac{1}{3}%$

(i)

(ii)

(iii)

(iv)

#### 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% = $7\frac{1}{2}%$

(ii)

(iii)

(iv)

#### 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

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{\mathrm{Profit}}{\mathrm{CP}}×100%$$=\frac{375}{12500}×100%=3%$

#### 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?

#### 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.

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% = $\frac{\mathrm{Gain}}{\mathrm{CP}}×100%=\frac{190}{1520}×100%=12\frac{1}{2}%$

#### 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.

#### 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.

#### Question 9:

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

#### Question 10:

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

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{\mathrm{SP}-\mathrm{CP}}{\mathrm{CP}}×100%=\frac{\left(130x-125x\right)}{125x}×100%$$=\frac{5x}{125x}×100%=4%$
Thus, the gain percent is 4%.

#### Question 11:

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

#### Question 12:

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

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 = $12×\frac{10}{3}=₹40$
SP of 4 oranges = ₹18
SP of 1 orange = $\frac{18}{4}=₹\frac{9}{2}$
SP of 12 oranges = $12×\frac{9}{2}=₹54$
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP − CP = ₹54 − ₹40 = ₹14
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}×100%=\frac{14}{40}×100%=35%$

#### Question 13:

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

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 = $60×\frac{10}{3}=₹200$
SP of 10 bananas = ₹36
∴ SP of 1 banana = $\frac{36}{10}=₹\frac{18}{5}$
⇒ SP of 60 bananas = $60×\frac{18}{5}=₹216$
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP − CP = ₹216 − ₹200 = ₹16
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}×100%=\frac{16}{200}×100=8%$

#### Question 14:

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

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 = $60×\frac{75}{10}=₹450$
SP of 12 oranges = ₹75
∴ SP of 1 orange = $₹\frac{75}{12}$
⇒ SP of 60 oranges = $60×\frac{75}{12}=₹375$
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP − SP = ₹450 − ₹375 = ₹75
∴ Loss% = $\frac{\mathrm{Loss}}{\mathrm{CP}}×100%=\frac{75}{450}×100%=16\frac{2}{3}%$

#### 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?

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
$\therefore \frac{36}{5}x-\frac{16}{3}x=168\phantom{\rule{0ex}{0ex}}⇒\frac{28}{15}x=168\phantom{\rule{0ex}{0ex}}⇒x=\frac{168×15}{28}\phantom{\rule{0ex}{0ex}}⇒x=90$
Hence, the man purchased 90 eggs.

#### 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.

#### 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.

#### 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.

Let the cost price be ₹x.
Loss = 10% of ₹x = $\frac{10}{100}x=₹\frac{x}{10}$
SP in case of loss = CP − Loss = $x-\frac{x}{10}=₹\frac{9x}{10}$
Gain =10% of ₹x = $\frac{10}{100}x=₹\frac{x}{10}$
SP in case of profit = CP + Profit = $x+\frac{x}{10}=₹\frac{11x}{10}$
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
$⇒\frac{11x}{10}-\frac{9x}{10}=940\phantom{\rule{0ex}{0ex}}⇒\frac{2x}{10}=940\phantom{\rule{0ex}{0ex}}⇒x=4700$
Hence, the cost price of the table is ₹4,700.

#### 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.

#### 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.

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
$\therefore \frac{114x}{100}-\frac{110x}{100}=260\phantom{\rule{0ex}{0ex}}⇒\frac{4x}{100}=260\phantom{\rule{0ex}{0ex}}⇒x=6500$
Hence, the CP of the cycle is ₹6,500.

#### 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?

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 = $\frac{5}{100}×920=₹46$
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.

#### 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.

CP of the first bat = ₹840
Profit% on the first bat = 15%
∴ Profit = 15% of ₹840 = $\frac{15}{100}×840=₹126$
SP of the first bat = ₹840 + ₹126 = ₹966
CP of the second bat = ₹360
Loss = 5% of ₹360 = $\frac{5}{100}×360=₹18$
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$=\frac{108}{1200}×100=9%$

#### 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.

CP of first jeans = ₹1,450
Profit = 8% of CP = $\frac{8}{100}×1450=₹116$
SP of first jeans = ₹1,450 + ₹116 = ₹1,566
CP of second jeans = ₹1,450
Loss = 4% of CP = $\frac{4}{100}×1450=₹58$
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% =

#### 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?

CP of 1 kg of rice = Rs 25
C.P of 200 kg rice=
CP of 80 kg of rice=

CP of 40 kg of rice =

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

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

#### 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.

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

#### Question 26:

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

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

#### Question 27:

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

SP of the bouquet = Rs 322
Gain percentage = 15%

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

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

#### Question 28:

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

Let the CP of the umbrella be ₹x.
SP of the umbrella = ₹336
Loss = 4% of ₹x = $₹\frac{4}{100}x$
CP − Loss = SP
$⇒x-\frac{4}{100}x=336\phantom{\rule{0ex}{0ex}}⇒\frac{96}{100}x=336\phantom{\rule{0ex}{0ex}}⇒x=₹350$
∴ CP of the umbrella = ₹350
Now, for gain of 4%,
SP = CP + Gain
$⇒\mathrm{SP}=350+\frac{4}{100}×350\phantom{\rule{0ex}{0ex}}⇒\mathrm{SP}=350+14\phantom{\rule{0ex}{0ex}}⇒\mathrm{SP}=₹364$
Hence, in order to gain 4%, the umbrella should be sold for ₹364.

#### 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?

Let the original price be $x$.
SP = Rs 3120
Now, SP = CP − loss
$⇒3120=x-\frac{4}{\frac{100}{x}}\phantom{\rule{0ex}{0ex}}⇒3120=x-\frac{x}{25}\phantom{\rule{0ex}{0ex}}⇒3120=\frac{24x}{25}\phantom{\rule{0ex}{0ex}}⇒\frac{3120×25}{24}=x\phantom{\rule{0ex}{0ex}}⇒x=3250\phantom{\rule{0ex}{0ex}}$

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

Hence, gain percent = 6%

#### 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.

SP of first saree = ₹1,980
Loss = 10%
Let the CP of first saree be ₹x.
CP = Loss + SP
$⇒\frac{10}{100}×x+1980=x\phantom{\rule{0ex}{0ex}}⇒x-\frac{10}{100}x=1980\phantom{\rule{0ex}{0ex}}⇒\frac{90}{100}x=1980\phantom{\rule{0ex}{0ex}}⇒x=2200$
∴ 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
$⇒1980-\frac{10}{100}×y=y\phantom{\rule{0ex}{0ex}}⇒1980-\frac{y}{10}=y\phantom{\rule{0ex}{0ex}}⇒y+\frac{y}{10}=1980\phantom{\rule{0ex}{0ex}}⇒\frac{11y}{10}=1980\phantom{\rule{0ex}{0ex}}⇒y=1800$
∴ 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

#### 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.

SP of first fan = ₹1,140
Gain = 14%
Let the CP of first fan be ₹x.
CP = SP − Gain
$⇒x=1140-\frac{14}{100}x\phantom{\rule{0ex}{0ex}}⇒x+\frac{14}{100}x=1140\phantom{\rule{0ex}{0ex}}⇒\frac{114}{100}x=1140\phantom{\rule{0ex}{0ex}}⇒x=1000$
∴ 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
$⇒y=\frac{5}{100}y+1140\phantom{\rule{0ex}{0ex}}⇒y-\frac{5}{100}y=1140\phantom{\rule{0ex}{0ex}}⇒\frac{95}{100}y=1140\phantom{\rule{0ex}{0ex}}⇒y=1200$
∴ 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

#### 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?

Let the CP of the watch for Vinod be ₹x.
SP = Gain + CP

Now,
SP of the water for Vinod will be the CP of the watch for Arun.
SP of the watch for Arun
= CP − Loss

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,
$\frac{112}{100}x\left(\frac{95}{100}\right)=3990$
$⇒x=\frac{3990×100×100}{112×95}=3750$
Thus, Vinod paid ₹3,750 for the watch.

#### 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?

CP of the plot of land = ₹4,80,000
CP of $\frac{2}{5}$th of the land = $\frac{2}{5}×480000=₹1,92,000$
Loss on $\frac{2}{5}$th of the land = 6%
SP of $\frac{2}{5}$th of the land = CP − Loss
$=192000-\frac{6}{100}×192000\phantom{\rule{0ex}{0ex}}=₹1,80,480$
CP of $\frac{3}{5}$th of the land = 480000 − 192000 = ₹2,88,000
Total gain% = 10%
Total gain = $\frac{10}{100}×480000=₹48,000$
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 =

#### 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?

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

CP of one-third of the sugar = Rs

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

At a profit of 12%, we have:

∴ 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

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

#### 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.

Marked price =  and discount = 18%
Discount = 18% of marked price

Selling price = marked price − discount

Therefore, the selling price of the cooler is .

#### 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.

Marked Price = Rs 960
Selling Price = Rs 816
Discount = MP − SP
= Rs (960 − 816)
= Rs 144

Therefore, the discount on the sweater is 15%.

#### 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.

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

#### 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.

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

∴ Marked price =

#### 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.

Cost price = Rs 528
Rate of discount = 12%
Marked price = ?
SP= MP − discount
Let the MP be Rs $x$.

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

#### 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.

Let Rs 100 be the CP.
Then, marked price =
Discount = 20% of MP
$=\frac{20}{100}×135\phantom{\rule{0ex}{0ex}}=27$
Selling price = marked price − discount
= 135 − 27
= Rs 108
Now, gain = SP − CP
=108 − 100
=Rs 8

=

#### 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.

Let Rs 100 be the CP.
Then, marked price =
Discount = 30% of MP
$=\frac{30}{100}×140\phantom{\rule{0ex}{0ex}}=42$
Selling Price = marked price − discount
= 140 − 42
= Rs 98
Now, loss = CP − SP
= 100 − 98
= Rs 2

Therefore, the shopkeeper had a loss of 2%.

#### 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.

Cost price of the fan =
Gain percentage = 25%

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

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

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

$⇒1350=\frac{100x-25x}{100}\phantom{\rule{0ex}{0ex}}⇒135000=75x⇒x=\frac{13500}{75}⇒x=1800$

Therefore, the marked price of the fan is .

#### 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.

Cost price of the refrigerator =
Gain percentage = 20%.

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

$⇒13818=\frac{100x-16x}{100}\phantom{\rule{0ex}{0ex}}⇒1381800=84x⇒x=\frac{1381800}{84}⇒x=16450$

​Therefore, the marked price of the refrigerator is .

#### 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.

The cost price of the ring is .
Gain percentage = 20%.

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

$⇒1428=x-\frac{16x}{100}\phantom{\rule{0ex}{0ex}}⇒1428=\frac{100x-16x}{100}\phantom{\rule{0ex}{0ex}}⇒142800=84x\phantom{\rule{0ex}{0ex}}⇒\frac{142800}{84}=x\phantom{\rule{0ex}{0ex}}⇒x=1700$

​Therefore, the marked price of the ring is .

#### 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?

Let be the cost price.
Gain required = 17%
∴ Selling price =
Let the marked price be .
Then, discount = 10% of x
$=\frac{10}{100}×x\phantom{\rule{0ex}{0ex}}=\frac{x}{10}$
Selling Price = MP − discount
$⇒117=x-\frac{x}{10}\phantom{\rule{0ex}{0ex}}⇒117=\frac{9x}{10}$

$⇒9x=1170\phantom{\rule{0ex}{0ex}}⇒x=\frac{1170}{9}\phantom{\rule{0ex}{0ex}}⇒x=130$

∴ Marked price =

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

#### 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%?

Let be the cost price.
Gain required = 8%
Therefore, the selling price is .
Let be the marked price.
Then, discount = 10% of x
$=\frac{10}{100}×x\phantom{\rule{0ex}{0ex}}=\frac{x}{10}$
Selling Price = MP − discount
$⇒117=x-\frac{x}{10}\phantom{\rule{0ex}{0ex}}⇒117=\frac{9x}{10}$

$⇒9x=1080\phantom{\rule{0ex}{0ex}}⇒x=\frac{1080}{9}\phantom{\rule{0ex}{0ex}}⇒x=120$

∴ Marked price =

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

#### 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?

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

Price after the first discount = Rs (18500 − 3700)= Rs 14800
Second discount = 5% of 14800
$=\frac{5}{100}×14800\phantom{\rule{0ex}{0ex}}=740$
Price after the second discount = (14800 − 740)
= Rs 14060
The TV is available for

#### Question 14:

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

​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

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:

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

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

Bill amount

Hence, the cost of the refrigerator is Rs 15,529.

#### 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.

(i)

$=\mathrm{Rs}.\left(250×\frac{6}{100}\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.15$

$=\mathrm{Rs}.265$

(ii)

$=\mathrm{Rs}.\left(625×\frac{4}{100}\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.25$

$=\mathrm{Rs}.473$

$=\mathrm{Rs}.1269$

#### Question 3:

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

Let the original price of the watch be Rs x.
VAT = 10% of Rs x

∴ Price including VAT =

Now, $\frac{11x}{10}=1980$

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

#### Question 4:

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

​​Let the original price of the shirt be Rs x.
VAT = 7% of Rs x
$=\mathrm{Rs}.\left(x×\frac{7}{100}\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\frac{7x}{100}$
∴ Price including VAT = $\mathrm{Rs}.\left(x+\frac{7x}{100}\right)$
$=\mathrm{Rs}.\frac{107x}{100}$
Now, $\frac{107x}{100}=1337.50$

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

#### Question 5:

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

Let the price of 10 g of gold be Rs x.

∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{x}{100}\right)$

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

#### Question 6:

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

Let the original price of the computer be Rs x.

∴ Price including VAT$=\mathrm{Rs}.\left(x+\frac{4x}{100}\right)$
$=\mathrm{Rs}.\frac{104x}{100}$

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

#### Question 7:

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

​Let the original cost of the spare parts be Rs x.

∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{12x}{100}\right)$
$=\mathrm{Rs}.\frac{112x}{100}$

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

#### 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?

​Let the list price of the TV set be Rs x.

∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{8x}{100}\right)\phantom{\rule{0ex}{0ex}}$
$=\mathrm{Rs}.\frac{108x}{100}$

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

#### 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.

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

∴ The rate of VAT is 5%.

#### 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.

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

∴ The rate of VAT is 8%.

#### 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.

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

∴ The rate of VAT is 12.5%.

#### Question 1:

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) $37\frac{1}{2}%$

#### Question 2:

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) $14\frac{1}{5}%$

#### Question 3:

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

#### 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

#### Question 5:

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%

(c) 120%

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

According to the question, we have:

SP = Rs 2x
∴ Gain percentage = $\frac{\mathrm{gain}}{\mathrm{CP}}×100\phantom{\rule{0ex}{0ex}}$

$=\frac{2x-\frac{10x}{11}}{\frac{10x}{11}}×100\phantom{\rule{0ex}{0ex}}=\frac{12}{10}×100\phantom{\rule{0ex}{0ex}}=120%$

#### Question 6:

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%

(d) 125%

#### Question 7:

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%

(c) 20%

$=\left(\frac{2x}{10x}×100\right)%\phantom{\rule{0ex}{0ex}}=20%$

#### Question 8:

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) $16\frac{2}{3}%$

(b) 25%

#### Question 9:

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%

(d) 150%

​
$=Rs.5$

#### Question 10:

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%

(d) 25%

​

#### Question 11:

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%

​(a) 4%

#### Question 12:

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%

(a) 20%

#### Question 13:

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

​ (b) Rs.1200

$=\mathrm{Rs}.\left\{\frac{\left(100+25\right)}{100}×960\right\}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\left(\frac{125}{100}×960\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.1200$

#### Question 14:

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) $6\frac{1}{4}%$

(a) 5%

#### Question 15:

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

(a) 1.5% gain

​
$=\mathrm{Rs}.\left\{\frac{100}{\left(100+20\right)}×500\right\}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\left(\frac{100}{120}×500\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.416.67$

$=\mathrm{Rs}.\left\{\frac{100}{\left(100-12\right)}×500\right\}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\left(\frac{100}{88}×500\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.568.18$

$=Rs.984.85$

$=Rs.1000$

#### Question 16:

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

(b) Rs 530

#### Question 17:

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

​(c) Rs 198

$=\mathrm{Rs}.\left\{\frac{\left(100+20\right)}{100}×165\right\}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\left(\frac{120}{100}×165\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.198$

#### Question 18:

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

(a)​ Rs. 50

#### Question 19:

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) $8\frac{1}{4}%$

​(b) 8%

#### Question 20:

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

​(c) 1% loss

#### Question 21:

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

(c) Rs.750

$=Rs.\frac{11x}{10}\phantom{\rule{0ex}{0ex}}$

$⇒x=\left(825×\frac{10}{11}\right)\phantom{\rule{0ex}{0ex}}⇒x=750$

∴ The basic price of the watch is Rs 750.

#### Question 1:

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

$=\mathrm{Rs}.\left\{\frac{100}{\left(100+15\right)}×322\right\}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\left(\frac{100}{115}×322\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.280$

$=\mathrm{Rs}.\left\{\frac{\left(100+20\right)}{100}×280\right\}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\left(\frac{120}{100}×280\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.336$

∴ The desired selling price is Rs 336.

#### Question 2:

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

#### 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.

#### Question 4:

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

#### Question 5:

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

$=Rs.80$

$=\mathrm{Rs}.72$

$=28%$

#### Question 6:

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

​
$=\mathrm{Rs}.\frac{11x}{10}$

$⇒x=\left(1870×\frac{10}{11}\right)\phantom{\rule{0ex}{0ex}}⇒x=1700$

#### 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%

(b) 25%
​

#### 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%

(d) 25%

#### 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%

(b) 20%

#### 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

(c) Rs.920

$=\mathrm{Rs}.\left\{\frac{100}{\left(100-15\right)}×680\right\}\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.\left(\frac{100}{85}×680\right)\phantom{\rule{0ex}{0ex}}=\mathrm{Rs}.800$

#### 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%

​(c) 8%

#### 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

​(c) Rs.750

$=Rs.\frac{108x}{100}$

$⇒x=\left(810×\frac{100}{108}\right)\phantom{\rule{0ex}{0ex}}⇒x=750$

#### 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.

​(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:

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

​(i) False (F)

$\mathrm{SP}=\left\{\frac{\left(100-\mathrm{loss}%\right)}{100}×\mathrm{CP}\right\}$

(ii) True (T)

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

(iv) True (T)

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