myhelper: RS Aggarwal 2019,2020 solution class 7 chapter 11 Profit and Loss Exercise 11B

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RS Aggarwal 2019,2020 solution class 7 chapter 11 Profit and Loss Exercise 11B

Exercise 11B

Page-158

Question 1:

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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 1:

(b) 25%

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

Question 2:

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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 2:

(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
$Loss % = (\frac{Loss}{CP} \times 100) % = (\frac{15}{120} \times 100) % = \frac{25}{2} % = 12 \frac{1}{2} %$

Question 3:

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On selling a bat for Rs 100, a man gains Rs 20. His gain % is

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

Answer 3:

(b) 25%

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

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

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

Question 4:

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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 4:

(a) Rs. 180

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

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

Question 5:

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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 5:

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.

Question 6:

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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 6:

(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%:

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

Question 7:

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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 7:

(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 = $Rs (15 - 12) = Rs 3$

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

Question 8:

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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 8:

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

Question 9:

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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 9:

(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-159

Question 10:

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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 10:

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

Question 11:

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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 11:

(d)Rs. 600

SP of the chair = Rs 720
Gain% = 20

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

Question 12:

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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 12:

(c) Rs. 700

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