Rs Aggarwal 2019 2020 for Class 7 Math Chapter 11 - Profit And Loss

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Rs Aggarwal 2019 2020 Solutions for Class 7 Math Chapter 11 Profit And Loss are provided here with simple step-by-step explanations. These solutions for Profit And Loss are extremely popular among Class 7 students for Math Profit And Loss Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2019 2020 Book of Class 7 Math Chapter 11 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2019 2020 Solutions. All Rs Aggarwal 2019 2020 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

Page No 157:

Question 1:

Find the SP when:

(i) CP = Rs 950, gain = 6%
(ii) CP = Rs 9600, gain = $16 \frac{2}{3} %$
(iii) CP = Rs 1540, loss = 4%
(iv) CP = Rs 8640, loss = $12 \frac{1}{2} %$

Answer:

(i) CP = Rs. 950
Gain = 6%

$SP = {\frac{(100 + G ain %)}{100} \times CP} = {\frac{(100 + 6)}{100} \times 950} = \frac{106}{100} \times 950 = \frac{100700}{100} = Rs . 1007$

(ii) CP = Rs. 9600
Gain = $16 \frac{2}{3} % = \frac{50}{3} %$

$S P = {\frac{(100 + G ain %)}{100} \times CP} = {\frac{(100 + \frac{50}{3})}{100} \times 9600} = \frac{350}{300} \times 9600 = \frac{3360}{3} = Rs . 11200$

(iii) CP = Rs. 1540
Loss = 4%

$S P = {\frac{(100 - L oss %)}{100} \times CP} = {\frac{(100 - 4)}{100} \times 1540} = \frac{96}{100} \times 1540 = \frac{147840}{100} = Rs . 1478.40$

(iv) CP = Rs. 8640
Loss = $12 \frac{1}{2} % = \frac{25}{2} %$

$S P = {\frac{(100 - L oss %)}{100} \times CP} = {\frac{(100 - \frac{25}{2})}{100} \times 8640} = \frac{175}{200} \times 8640 = \frac{1512000}{200} = Rs . 7560$

Page No 157:

Question 2:

Find the gain or loss per cent when:

(i) CP = Rs 2400 and SP = Rs 2592
(ii) CP = Rs 1650 and SP = Rs 1452
(iii) CP = Rs 12000 and SP = Rs 12800
(iv) CP = Rs 1800 and SP = Rs 1611

Answer:

(i) CP = Rs. 2400
SP = Rs. 2592
Gain = SP - CP = Rs. ( 2592 - 2400) = Rs. 192

Gain% = $(\frac{Gain}{CP} \times 100)$ $= (\frac{192}{2400} \times 100)$ = $8$

(ii) CP = Rs. 1650
SP = Rs. 1452
Loss = CP - SP = ( 1650 - 1452) = Rs. 198

   Loss% = $(\frac{L oss}{CP} \times 100)$ $= (\frac{198}{1650} \times 100) = 12$

(iii) CP = Rs. 12000 and SP = Rs. 12800
Gain = SP - CP = ( 12800 - 12000) = Rs. 800

   Gain% = $(\frac{Gain}{CP} \times 100) =$ $(\frac{800}{12000} \times 100) = 6.66$

(iv) CP = Rs. 1800
SP = Rs. 1611
Loss = CP - SP = ( 1800 - 1611) = Rs. 189

   Loss% = $(\frac{L oss}{CP} \times 100) =$ $(\frac{189}{1800} \times 100) = 10.5$

Page No 157:

Question 3:

Find the CP when:

(i) SP = Rs 924, gain = 10%
(ii) SP = Rs 1755, gain = $12 \frac{1}{2} %$
(iii) SP = Rs 8510, loss = 8%
(iv) SP = Rs 5600, loss = $6 \frac{2}{3} %$

Answer:

(i) SP = Rs. 924
Gain = 10%

$CP = {\frac{100}{(100 + G ain %)} \times SP}$

$= {\frac{100}{(100 + 10)} \times 924} = \frac{92400}{110} = Rs . 840$

(ii) SP = Rs. 1755
Gain = $12 \frac{1}{2} % = \frac{25}{2} %$

$CP = {\frac{100}{(100 + G ain %)} \times SP} = {\frac{100}{(100 + \frac{25}{2})} \times 1755} = {\frac{200}{225} \times 1755} = \frac{351000}{225} = Rs . 1560$

(iii) SP = Rs. 8510
Loss = 8%

$CP = {\frac{100}{(100 - L oss %)} \times SP} = {\frac{100}{(100 - 8)} \times 8510} = \frac{851000}{92} = Rs . 9250$

(iv) SP = Rs. 5600
Loss = $6 \frac{2}{3} % = \frac{20}{3} %$

$CP = {\frac{100}{(100 - L oss %)} \times SP} = {\frac{100}{(100 - \frac{20}{3})} \times 5600} = {\frac{300}{280} \times 5600} = \frac{168000}{28} = Rs . 6000$

Page No 157:

Question 4:

Sudhir bought an almirah for Rs 13600 and spent Rs 400 on its transportation. He sold it for Rs 16800. Find his gain per cent.

Answer:

Cost price of an almirah = Rs. 13600
Transportation cost = Rs. 400
Total cost price = Rs. (13600 + 400) = Rs. 14000
Selling price = Rs. 16800
Now, SP > CP
$Gain = SP - CP =$ ( 16800 - 14000) = Rs. 2800

$Gain % = (\frac{Gain}{CP} \times 100)$ %

$= (\frac{2800}{14000} \times 100)$ %

$= \frac{2800}{140} % = 20 %$

Page No 157:

Question 5:

Ravi purchased an old house for Rs 765000 and spent Rs 115000 on its repairs. Then, he sold it at a gain of 5%. How much did he get?

Answer:

Cost price of the house = Rs. 765000
Cost of repairing the house = Rs. 115000
Total Cost price = (765000 + 115000) = Rs. 880000
Ravi sold it at a gain of 5%.

$SP = {\frac{(100 + gain %)}{100} \times CP} = {\frac{(100 + 5)}{100} \times 880000} = \frac{105}{100} \times 880000 = Rs . 924000$

He gets Rs. 924000.

Page No 157:

Question 6:

A vendor busy lemons at Rs 25 per dozen and sells them at the rate of 5 for Rs 12. Find his gain or loss per cent.

Answer:

CP of 12 lemons (dozen) = Rs. 25
CP of one lemon = Rs. $\frac{25}{12}$

CP of five lemons = 5 × $\frac{25}{12} =$ $\frac{125}{12} = Rs . 10.42$

SP of five lemons = Rs. 12 (given)

Gain = SP - CP = ( 12 - 10.42 ) = Rs 1.58

$Gain % = (\frac{Gain}{CP} \times 100)$ %

$= (\frac{1.58}{10.42} \times 100)$ %

= 15.2%

Page No 157:

Question 7:

The selling price of 12 pens is equal to the cost price of 15 pens. Find the gain per cent.

Answer:

Let the cost price of the pen be Re 1.
Cost price of 12 pens = Rs 12
SP of 12 pens = CP of 15 pens = Rs 15
Gain = SP - CP = Rs (15 - 12) = Rs 3

$Gain % = (\frac{Gain}{CP} \times 100)$ %

$= (\frac{3}{12} \times 100) % = 25 %$

Gain% = 25%

Page No 157:

Question 8:

The selling price of 16 spoons is equal to the cost price of 15 spoons. Find the loss per cent.

Answer:

Let the cost price of one spoon be Re 1.
CP of 16 spoons = Rs 16
SP of 16 spoons = CP of 15 spoons = Rs 15
Loss = CP - SP = (16 - 15) = Re 1

$Loss % = (\frac{Loss}{CP} \times 100) % = (\frac{1}{16} \times 100) % = 6.25 %$

Loss% = 6.25%

Page No 157:

Question 9:

Manoj purchased a video for Rs 12000. He sold it to Rahul at a gain of 10%. If Rahul sells it to Rakesh at a loss of 5%, what did Rakesh pay for it?

Answer:

Cost price of a video = Rs. 12000
SP of a video at a gain of 10% = ${\frac{(100 + Gain %)}{100} \times CP}$

$= {\frac{(100 + 10)}{100} \times 12000} = {\frac{110}{100} \times 12000} = Rs . 13200$

So, Rahul purchased at a cost price of Rs. 13200.

Rahul sells it at a loss of 5%.

SP of a video at loss of 5% = ${\frac{(100 - Loss %)}{100} \times CP}$

$= {\frac{(100 - 5)}{100} \times 13200} = \frac{95}{100} \times 13200 = Rs . 12540$

∴ Rakesh pays = Rs. 12540

Page No 157:

Question 10:

On selling a sofa-set for Rs 21600, a dealer gains 8%. For how much did he purchase it?

Answer:

SP of the sofa set = Rs. 21600
Gain% = 8

$CP of the sofa se t = {\frac{100}{(100 + G a i n %)} \times S P} = {\frac{100}{(100 + 8)} \times 21600} = \frac{2160000}{108} = R s . 20000$

He purchased it at the cost of Rs. 20000.

Page No 157:

Question 11:

On selling a watch for Rs 11400, a shopkeeper loss 5%. For how much did the purchase it?

Answer:

SP of the watch = Rs 11400
Loss% = 5

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

$= {\frac{100}{(100 - 5)} \times 11400} = \frac{11400}{95} = Rs . 12000$

He purchased it at the cost of Rs. 12000.

Page No 157:

Question 12:

On selling a calculator for Rs 1325, a man gains 6%. For how much should he sell it to gain 12%?

Answer:

SP of the calculator = Rs. 1325
Gain % = 6

CP of the calculator = ${\frac{100}{(100 + Gain %)} \times SP}$

$= {\frac{100}{(100 + 6)} \times 1325} = \frac{132500}{106} = Rs . 1250$

$SP of the calculator = {\frac{(100 + Gain %)}{100} \times CP} = {\frac{(100 + 12)}{100} \times 1250} = \frac{140000}{100} = Rs . 1400$

Page No 157:

Question 13:

On selling a computer for Rs 24480, a dealer loses 4%. For how much should he sell it to gain 4%?

Answer:

SP of a computer = Rs. 24480
Loss% = 4

$CP of the c omputer = {\frac{100}{(100 - Loss %)} \times SP} = {\frac{100}{(100 - 4)} \times 24480} = \frac{2448000}{96} = Rs . 25500$

In order to gain 4%:
$SP of the c omputer = {\frac{(100 + Gain %)}{100} \times CP} = {\frac{(100 + 4)}{100} \times 25500} = {\frac{104}{100} \times 25500} = \frac{2652000}{100} = Rs . 26520$

Page No 157:

Question 14:

A tricycle is sold at a gain of 15%. Had it been sold for Rs 108 more, the profit would have been 20%. Find its cost price.

Answer:

Let the CP of the tricycle be Rs. x

SP at 15% gain = ${\frac{(100 + G ain %)}{100} \times CP}$
$= {\frac{(100 + 15)}{100} \times x} = \frac{115}{100} x$

$= Rs . \frac{23}{20} x$

SP at 20% gain = $x \times \frac{120}{100} =$ $Rs . \frac{6}{5} x$

$\frac{6}{5} x - \frac{23}{20} x = 108 \Rightarrow \frac{24 x - 23 x}{20} = 108 \Rightarrow \frac{x}{20} = 108 \Rightarrow x = 2160$

Hence, the cost price of the tricycle is Rs. 2160

Page No 157:

Question 15:

Sandeep sold a television at a loss of 8%. If he had sold it for Rs 3360 more, he would have gained 6%. For how much did Sandeep buy it?

Answer:

Let CP of a television be Rs x.
SP at 8% loss = $\frac{(100 - 8)}{100} \times x = Rs . \frac{92}{100} x$
100
SP at 6% gain = $(\frac{100 + 6)}{100} \times x = Rs . \frac{106}{100} x$

      $\frac{106}{100} x - \frac{92}{100} x = 3360$

⇒ $\frac{14}{100} x = 3360$

⇒ $x = \frac{336000}{14} = 24000$

∴ CP = Rs. 24000
Sandeep bought it at the cost of Rs. 24000.

Page No 157:

Question 16:

Pankaj sells two cycles for Rs 2376 each. On one he gains 10% and on the other he loss 10%. Find his gain or loss per cent.

Answer:

SP of each cycle = Rs. 2376
He gains 10% in one cycle.
CP = ${\frac{100}{(100 + G ain %)} \times SP}$
$= {\frac{100}{(100 + 10)} \times 2376} = \frac{100}{110} \times 2376 = Rs . 2160$

He looses 10% in the second cycle.
CP = $\frac{100}{(100 - L oss %)} \times SP$

$= \frac{100}{(100 - 10)} \times 2376 = \frac{100}{90} \times 2376 = \frac{23760}{9} = Rs . 2640$

Total CP = $Rs . (2160 + 2640) = Rs . 4800$
Total SP = $Rs . (2376 + 2376) = Rs . 4752$
Loss = CP - SP = $Rs . (4800 - 4752) = Rs . 48$
$Loss %$ = $(\frac{Loss}{CP} \times 100)$ %
$= (\frac{48}{4800} \times 100) % = 1 %$

Page No 157:

Question 17:

On selling an exhaust fan for Rs 7350, a man gains $\frac{1}{6}$ of its cost price. Find the cost price of the fan.

Answer:

Let the CP of the exhaust fan be Rs. x.
Gain = $Rs . \frac{x}{6}$

SP = $R s (x + \frac{x}{6})$

SP = Rs. 7350

∴ $x + \frac{x}{6} = 7350$
⇒ $\frac{7}{6} x = 7350$
⇒ $x = \frac{7350 \times 6}{7} = \frac{44100}{7} = 6300$
CP of the fan = Rs. 6300

Page No 157:

Question 18:

Mohit sold a watch to Karim at a gain of 10% and Karim sold it to Rahim at a gain of 4%. If Rahim pays Rs 14300 for it, for how much did Mohit purchase it?

Answer:

Mohit sold a watch to Karim at Rs. x.
Mohit sold it at a gain of 10%.
SP of the watch = $110 % o f x$
= $(x + \frac{110}{100}) = Rs . \frac{11}{20} x$
Karim sold it to Rahim at a gain of 4%.
SP of the watch = $104 % o f \frac{11}{10} x = (\frac{104}{100} \times \frac{11}{10} x) = Rs . (\frac{26}{25} \times \frac{11}{10} x)$

But, Rahim pays Rs. 14300.
∴ $\frac{26}{25} \times \frac{11}{10} x = 14300$

$\Rightarrow x = \frac{14300 \times 25 \times 10}{26 \times 11} = \frac{3575000}{286} = 12500$

Mohit purchased it at Rs. 25000.

Page No 157:

Question 19:

If the manufacturer gains 10%, the wholesale dealer 15%, and the retailer 25% then what is the production cost of a washing machine whose retail price is Rs 37950?

Answer:

Let the production cost of a washing machine be Rs. x.
Profit of the manufacturer = 10%
SP of the manufacturer = $110 % o f x$
= $(x + \frac{110}{100}) = \frac{110}{100} x = Rs . \frac{11}{10}$
Profit of the wholesale dealer = 15%
SP of the wholesale dealer = $115 % o f R s \frac{11}{10} x$
= $R s (\frac{11}{10} x \times \frac{115}{100}) = R s (\frac{11}{10} x \times \frac{23}{20})$

Profit of the retailer = 25%
SP of the retailer = $125 % o f R s (\frac{11}{10} x \times \frac{23}{20})$

= $Rs . (\frac{11}{10} x \times \frac{23}{20} \times \frac{125}{100}) = Rs . (\frac{11}{10} x \times \frac{23}{20} \times \frac{5}{4})$

Given:
Retail price = Rs. 37950
∴ $(\frac{11}{10} x \times \frac{23}{20} \times \frac{5}{4}) = 37950$

$\Rightarrow x = \frac{37950 \times 10 \times 20 \times 4}{11 \times 23 \times 5}$
=> x= $\frac{30360000}{1265} = 24000$

∴ Production cost of a washing machine = Rs. 24000

Page No 157:

Question 20:

Mr Mehta purchased a video for Rs 20000 and a television for Rs 30000. On the video he lost 5% and on the television he gained 8%. Find his total gain or loss per cent.

Answer:

Mr. Mehta purchased a video at the cost of Rs. 20000.
Mr. Mehta purchased a television at the cost of Rs. 30000.
Total cost = Rs. (20000 + 30000) = Rs. 50000

He lost 5% on the video.

$SP = \frac{(100 - L oss %)}{100} \times CP = \frac{100 - 5}{100} \times 20000 = \frac{95}{100} \times 20000 = Rs . 19000$

He gained 8% on the television.

$SP = \frac{(100 + G ain %)}{100} \times CP = \frac{100 + 8}{100} \times 30000 = \frac{108}{100} \times 30000 = Rs . 32400$

Total SP = $Rs . (190000 + 32400) = Rs . 51400$

Total CP = Rs. 50000
Total Gain = SP - CP = $Rs . (51400 - 50000) = Rs . 1400$
$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{1400}{50000} \times 100) % = 2.8 %$

Page No 158:

Question 21:

By selling 36 oranges, a vendor suffers a loss equal to the selling price of 4 oranges. Find his loss per cent.

Answer:

Let the CP of 1 orange be Rs. x.
∴ CP of 36 oranges = Rs. 36x
Let SP of orange be Rs. y.
∴ SP of 36 oranges = Rs. 36y

Loss = SP of 4 oranges = $4 y$      (given)

We know:
Loss = CP - SP
⇒    $4 y = 36 x - 36 y$
⇒ $4 y + 36 y = 36 x$
  ⇒    $40 y = 36 x$
⇒ $10 y = 9 x$
⇒ $y = \frac{9}{10} x$

$Loss % = (\frac{Loss}{CP} \times 100)$ %

$= (\frac{4 y}{36 x} \times 100)$ %

$= (\frac{4 \times 9 x}{36 x \times 10} \times 100) % = 10 %$

Loss% = 10%

Page No 158:

Question 22:

By selling 8 dozen pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain per cent.

Answer:

Let the CP of one pencil be Rs. x.
Therefore, the CP of 96 pencils will be Rs. 96x.
Let SP of one pencil be Rs. y.
∴ SP of 96 pencils = Rs. 96y
Gain= SP of one dozen pencil = Rs.12y           (given)

Gain = SP - CP

   $\Rightarrow 12 y = 96 y - 96 x \Rightarrow 96 x = 96 y - 12 y \Rightarrow 96 x = 84 y \Rightarrow x = \frac{84 y}{96}$

$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{12 y}{96 x} \times 100) % = (\frac{12 y \times 96}{96 \times 84 y} \times 100) % = 14.28 %$

Page No 158:

Question 1:

Mark (✓) against the correct answer
A man buys a book for Rs 80 and sells it for Rs 100. His gain % is

(a) 20%
(b) 25%
(c) 120%
(d) 125%

Answer:

(b) 25%

CP of the book = Rs. 80
SP of the book = Rs. 100
Gain = SP - CP = Rs. (100 - 80) = Rs. 20
$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Page No 158:

Question 2:

Mark (✓) against the correct answer
A football is bought for Rs 120 and sold for Rs 105. The loss % is

(a) $12 \frac{1}{2} %$
(b) $14 \frac{2}{7} %$
(c) $16 \frac{2}{3} %$
(d) $13 \frac{1}{3} %$

Answer:

(a) $12 \frac{1}{2} %$

CP of a football = Rs. 120
SP of a football = Rs. 105

CP>SP
∴ Loss = CP - SP = Rs. ( 120 - 105 ) = Rs. 15
$Loss % = (\frac{Loss}{CP} \times 100) % = (\frac{15}{120} \times 100) % = \frac{25}{2} % = 12 \frac{1}{2} %$

Page No 158:

Question 3:

Mark (✓) against the correct answer
On selling a bat for Rs 100, a man gains Rs 20. His gain % is

(a) 20%
(b) 25%
(c) 18%
(d) 22%

Answer:

(b) 25%

SP of the bat = Rs. 100
Gain = Rs. 20

Gain = SP - CP
⇒ 20 = 100 - CP
⇒ CP = 100 - 20 = Rs. 80

$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Page No 158:

Question 4:

Mark (✓) against the correct answer
On selling a racket for Rs 198, a shopkeeper gains 10%. The cost price of the racket is

(a) Rs 180
(b) Rs 178.20
(c) Rs 217.80
(d) Rs 212.50

Answer:

(a) Rs. 180

SP of the racket = Rs. 198
Gain% = 10

$CP of the r acket = {\frac{100}{(100 + Gain %)} \times 100} = {\frac{100}{(100 + 10)} \times 198} = \frac{100}{110} \times 198 = Rs . 180$

Page No 158:

Question 5:

Mark (✓) against the correct answer
On selling a jug for Rs 144, a man loses $\frac{1}{7}$ of his outlay. If it is sold for Rs 189, what is the gain%?

(a) 50%
(b) 25%
(c) 30%
(d) 12%

Answer:

Let the cost price be Rs. x.
Loss = $Rs . \frac{x}{7}$
∴ SP = $(x - \frac{x}{7}) = Rs . \frac{6}{7} x$

Given:
SP = Rs. 144

∴   $\frac{6}{7} x = 144$
⇒ $x = \frac{144 \times 7}{6} = Rs . 168$

∴ CP = Rs. 168
SP = Rs. 144

New SP = Rs. 189
Gain = SP - CP = $Rs . (189 - 168) = Rs . 21$

$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{21}{168} \times 100) % = 12.5 %$

The correct answer is 12.5%.
All the given options are wrong.

Page No 158:

Question 6:

Mark (✓) against the correct answer
On selling a pen 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 of the pen = Rs. 48
Loses = 20%
Then , $CP = {\frac{100}{(100 - Loss %)} \times SP}$
$= {\frac{100}{(100 - 20)} \times 48} = Rs . 60$

In order to gain 20%:

$SP = {\frac{(100 + Gain %)}{100} \times CP} = {\frac{(100 + 20)}{100} \times 60} = \frac{120}{100} \times 60 = Rs . 72$

Page No 158:

Question 7:

Mark (✓) against the correct answer
If the cost price of 12 pencils is equal to the selling price of 15 pencils, then the loss% is

(a) 20%
(b) 25%
(c) 3%
(d) $16 \frac{2}{3} %$

Answer:

(a) 20%

Let the cost price of each pencil be Rs.1
Cost of 15 pencils = Rs 15
SP of 15 pencil = CP of 12 pencil = Rs 12
∴ CP = Rs 15
SP = Rs 12

Loss = CP - SP = $Rs (15 - 12) = Rs 3$

$Los s % = (\frac{Loss}{CP} \times 100) % = (\frac{3}{15} \times 100) % = \frac{300}{15} % = 20 %$

Page No 158:

Question 8:

Mark (✓) against the correct answer
If the cost price of 4 toffees be equal to the selling price of 3 toffees, then the gain% is

(a) 25%
(b) 30%
(c) $16 \frac{2}{3} %$
(d) $33 \frac{1}{3} %$

Answer:

(d) $33 \frac{1}{3} %$

Let the cost price of each toffee be Rs. 1
Cost price of three toffees = Rs 3
SP of three toffees = CP of four toffees = Rs 4

CP = Rs 3
SP = Rs 4

Gain = SP - CP = $Rs (4 - 3) = Re 1$
$G a i n % = (\frac{G a i n}{C P} \times 100) % = (\frac{1}{3} \times 100) % = \frac{100}{3} % = 33 \frac{1}{3} %$

Page No 158:

Question 9:

Mark (✓) against the correct answer
On selling an article for Rs 144 a man loses 10%. At what price should he sell it to gain 10%?

(a) Rs 158.40
(b) Rs 172.80
(c) Rs 176
(d) Rs 192

Answer:

(c) Rs. 176

SP of an article = Rs. 144
Loss% = 10
$C P = {\frac{100}{(100 - Loss %)} \times S P} = {\frac{100}{(100 - 10)} \times 144} = \frac{100}{90} \times 144 = \frac{1440}{9} = Rs . 160$

In order to gain 10%:

$S . P . = \frac{(100 + Gain %)}{100} \times C P = \frac{(100 + 10)}{100} \times 160 = \frac{110}{100} \times 160 = Rs . 176$

Page No 159:

Question 10:

Mark (✓) against the correct answer
A vendor bought lemons at 6 for a rupee and sold them at 4 for a rupee. His gain % is

(a) 50%
(b) 40%
(c) $33 \frac{1}{3} %$
(d) $16 \frac{2}{3} %$

Answer:

(a) 50%

CP of six lemons = Re 1
CP of one lemon = $Rs \frac{1}{6}$

CP of four lemon = $Rs \frac{4}{6}$
SP of four lemon = Re 1

Gain = $1 - \frac{4}{6} = \frac{2}{6} = Rs \frac{1}{3}$
$Gain % = (\frac{Gain}{C P} \times 100) = (\frac{3}{2 \times 3} \times 100) = \frac{100}{2} = 50$

Page No 159:

Question 11:

Mark (✓) against the correct answer
On selling a chair for Rs 720, a man gains 20%. The cost price of the chair is

(a) Rs 864
(b) Rs 576
(c) Rs 650
(d) Rs 600

Answer:

(d)Rs. 600

SP of the chair = Rs 720
Gain% = 20

$C . P . = {\frac{100}{(100 + Profit percentage)} \times S . P .} = {\frac{100}{120} \times 720} = \frac{7200}{12} = Rs . 600$

Page No 159:

Question 12:

Mark (✓) against the correct answer
On selling a stool for Rs 630, a man loses 10%. The cost price of the stool is

(a) Rs 567
(b) Rs 693
(c) Rs 700
(d) Rs 730

Answer:

(c) Rs. 700

SP of a stool = Rs 630
Loss% = 10
$C P = {\frac{100}{(100 - L oss %)} \times S P} = {\frac{100}{(100 - 10)} \times 630} = \frac{100}{90} \times 630 = Rs 700$

Page No 160:

Question 1:

By selling a chair for Rs 1375 a man gains 10%. Find its cost price.

Answer:

SP of the chair = Rs 1375
Gain% = 10

$CP of the c hair = {\frac{100}{(100 + Gain %)} \times SP}$

$= {\frac{100}{(100 + 10)} \times 1375} = \frac{137500}{110} = Rs . 1250$

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Question 2:

If the selling price of 10 pens is equal to the cost price of 14 pens, find gain per cent.

Answer:

Let the cost of each pen be Rs. 1
CP of 10 pens = Rs. 10
SP of 10 pens = CP of 14 pens = Rs. 14
Gain = SP - CP = 14-10= Rs. 4
$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{4}{10} \times 100) % = 40 %$

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Question 3:

On selling a fan for Rs 2585 a man gains $\frac{1}{10}$ of its cost price. Find the cost price of tha fan.

Answer:

Let the cost price of the fan be Rs. x.
Gain = $Rs . \frac{x}{10}$
SP of the fan = $(x + \frac{x}{10}) = Rs . \frac{11}{10} x$
SP of the fan = $Rs . 2585$
∴ $\frac{11}{10} x = 2585$
⇒ $11 x = 25850$
⇒ $x = \frac{25850}{11} = 2350$

So, CP of the fan is Rs. 2350.

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Question 4:

A man buys lemons at 6 for Rs 10 and sells at 8 for Rs 15. Find his gain per cent.

Answer:

Cost price of six lemons = Rs. 10
Cost price of one lemon = $Rs . \frac{10}{6}$
Cost price of eight lemons = $8 \times \frac{10}{6} = Rs . \frac{80}{6} = Rs . 13.33$
Selling price of eight lemons = Rs. 15

$Gain = S P - C P = Rs . (15 - 13.33) = Rs . 1.67$

Gain% = $(\frac{Gain}{C . P .} \times 100)$ %
$= (\frac{1.67}{13.33} \times 100)$ %
$= 12.5$ %

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Question 5:

On selling a bat for Rs 486 a man loses 10%. Find the cost price of the bat.

Answer:

SP of the bat = Rs 486
Loss = 10%
CP of the bat = ${\frac{100}{(100 - Loss %)} \times S P}$
$= {\frac{100}{(100 - 10)} \times 486} = \frac{48600}{90} = Rs 540$

CP of the bat = Rs 540

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Question 6:

Mark (✓) against the correct answer
On selling a football for Rs 100, a man gains Rs 15. The cost price of the football is

(a) Rs 115
(b) Rs 85
(c) Rs 70
(d) Rs 130

Answer:

(b) Rs 85

SP of a football = Rs 100
Gain = Rs 15
Gain = SP - CP
⇒ 15 = 100 - CP
⇒ CP = Rs (100 - 15)
⇒ CP= Rs 85

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Question 7:

Mark (✓) against the correct answer
A vendor buys lemons at Rs 25 per dozen and sells at 5 for Rs 12. His gain per cent is

(a) 14.5%
(b) 15%
(c) 15.2%
(d) 16%

Answer:

(c) 15.2%

Cost price of 12 bananas = Rs. 25
Cost price of one banana = $Rs . \frac{25}{12}$
$Cost price of five banana s = Rs . 5 \times \frac{25}{12} = Rs . \frac{125}{12} = Rs . 10.42$

He sells five bananas at the cost (SP) of Rs. 12.
Gain = SP - CP

= $= Rs . (12 - 10.42) = Rs . 1.58$

$Gain % = (\frac{Gain}{C P} \times 100) % = (\frac{1.58}{10.4} \times 100) % = 15.2 %$

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Question 8:

Mark (✓) against the correct answer
On selling a jug for Rs 168, a man loses $\frac{1}{7}$ of his outlay. The cost price of the jug is

(a) Rs 144
(b) Rs 192
(c) Rs 196
(d) none of these

Answer:

(c) Rs. 196

Let the cost price of the jug be Rs. x.
Loss = $Rs . \frac{x}{7}$
SP of the jug = CP - Loss
$= Rs . (x - \frac{x}{7}) = Rs . \frac{6}{7} x$

SP of the jug = $R s 168$ (given)

∴ $\frac{6}{7} x = 168$
$\Rightarrow = \frac{168 \times 7}{6} \Rightarrow x = \frac{1176}{6} \Rightarrow x = 196$

∴ CP of the jug = $Rs . 196$

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Question 9:

Mark (✓) against the correct answer
If the cost price of 5 bananas be equal to the selling price of 3 bananas, then gain per cent is

(a) $33 \frac{1}{3} %$
(b) 15%
(c) $66 \frac{2}{3} %$
(d) 40%

Answer:

(c) $66 \frac{2}{3} %$

Let the cost price of each banana be Re 1.
Cost price of three bananas = Rs. 3
SP of three bananas = CP of five bananas = Rs. 5
Gain = SP - CP = $Rs . (5 - 3) = Rs . 2$

$Gain % = (\frac{Gain}{C P} \times 100) % = (\frac{2}{3} \times 100) % = (\frac{200}{3}) % = 66 \frac{2}{3} %$

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Question 10:

Fill in the blanks.

(i) Loss = (CP) − (......).
(ii) CP = $\frac{100 \times SP}{(. . . . . . + . . . . . .)}$ .
(iii) Profit or loss is always reckoned on ...... .
(iv) $\frac{100}{(100 - loss %)} \times SP = . . . . . . .$

Answer:

(i) Loss = (CP) - (SP)

(ii) CP = $\frac{100 \times S P}{(100 + Gain %)}$

(iii) Profit or loss is always reckoned on the cost price.
(iv) $\frac{100 \times SP}{(100 - loss %)}$ = CP

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Question 11:

Write 'T' for true and 'F' for false

(i) Loss is reckoned on selling price.
(ii) Gain is reckoned on cost price.
(iii) $CP = \frac{100 \times SP}{(100 - loss %)} .$
(iv) Loss = (CP) − (SP).

Answer:

(i) False
Gain or loss is always reckoned on the cost price.

(ii) True
(iii) True
(iv) True

View NCERT Solutions for all chapters of Class 7