# RS Aggarwal Solutions Class 7 Ex 11A

Mark the correct answer in each of the following:

Q1: 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%

Sol:

(b) 25%

CP of the book = Rs. 80

SP of the book = Rs. 100

Gain = SP – CP = Rs. (100 – 80) = Rs. 20

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

$=\left ( \frac{20}{80} \times 100 \right )\%$

= 25%

Q2: 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) $13 \frac{1}{3}$%

Sol:

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

CP of a football = Rs. 120

SP of a football = Rs. 105

CP > SP

Therefore, Loss = CP – SP = Rs. (120 – 105) = Rs. 15

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

= $\left ( \frac{15}{120} \times 100 \right )$%

$= \frac{25}{2}$%

= $12\frac{1}{2}$%

Q3: On selling a bat for Rs. 100, a man gains Rs. 20. His gain % is

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

Sol:

(b) 25%

SP of the bat = Rs. 100

Gain = Rs. 20

Gain = SP – CP

$\Rightarrow 20 = 100 – CP$

$\Rightarrow CP = 100 – 20 = Rs. 80$

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

= $\left ( \frac{20}{80} \times 100 \right )$ %

= 25%

Q4: 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) 217.80              (d) Rs. 212.50

Sol:

(a) Rs. 180

SP of the racket = Rs. 198

Gain % = 10

CP of the racket = $\left ( \frac{100}{\left ( 100 + Gain \% \right )} \times 100 \right )$

= $\left [ \frac{100}{\left ( 100 + 10\right )} \times 198 \right ]$

$= \frac{100}{110} \times 198$

= Rs. 180

Q5: 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) 12.5%                 (b) 25%                    (c) 30%                (d) 50%

Sol:

(a) 12.5%

Let the cost price be Rs. x.

Loss = Rs. $\frac{x}{7}$

Therefore, SP = $\left ( x – \frac{x}{7} \right ) = Rs. \frac{6}{7} x$

Given:

SP = Rs. 144

Therefore, $\frac{6}{7} x = 144$

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

Therefore, $CP = Rs. 168$

SP = Rs. 144

New SP = Rs. 189

Gain = SP – CP = Rs. (189 – 168) = Rs. 21

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

$= \left ( \frac{21}{168} \times 100 \right )$%

= 12.5%

Thus Gain% = 12.5%

Q6: On selling a pen for Rs. 48, a shopkeeper losses 20%. In order to gain 20% what would be his Selling price?

(a) Rs. 52                    (b) Rs. 56                   (c) Rs. 68               (d) Rs. 72

Sol:

(d) Rs. 72

SP of the pen = Rs. 48

Loses = 20%

Then, CP = $\left [ \frac{100}{100 – Loss \%} \times SP \right ]$

$\left [\frac{100}{100 – 20 \%} \times 48 \right ]$

= Rs. 60

In order to gain 20%

SP = $\left [ \frac{100 + Gain \%}{100} \times CP \right ]$

= $\left [ \frac{100 + 20}{100} \times 60 \right ]$

= $\frac{120}{100} \times 60$

= Rs. 72

Q7: 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)$16\frac{2}{3}$%

Sol:

(a) 20%

Let the cost price of each pencils be Re. 1

Cost of 15 pencils = Rs. 15

SP of 15 pencils = CP of 12 pencils = Rs. 12

Therefore, CP = Rs. 15

SP = Rs. 12

Loss = CP – SP = Rs. (15 – 12) = Rs. 3

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

$\left ( \frac{3}{15} \times 100 \right )$%

= $\frac{300}{15}$%

= 20%

Q8: 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) $33 \frac{1}{3}$%

Sol:

(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

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

$\left ( \frac{1}{3} \times 100 \right )$%

= $\frac{100}{3}$%

= $33 \frac{1}{3}$%

Q9: 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

Sol:

(c) Rs. 176

SP of an article = Rs. 144

Loss% = 10

CP = $\left [ \frac{100}{\left ( 100 – Loss \% \right )} \times SP \right ]$

= $\left [ \frac{100}{\left ( 100 – 10 \right )} \times 144 \right ]$

$= \frac{100}{90} \times 144$

= $\frac{1440}{9}$

= Rs. 160

In order to gain 10%,

SP = $\frac{100 + Gain \%}{100} \times CP$

= $\frac{100 + 10}{100} \times 160$

= $\frac{110}{100} \times 160$

= Rs. 176

Q10: 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) $16\frac{2}{3}$%

Sol:

(a) 50%

CP of six lemons = Re. 1

CP of one lemon = Rs. $\frac{1}{6}$

CP of four lemons = Rs. $\frac{4}{6}$

SP of four lemons = Re. 1

Gain = 1 – $\frac{4}{6}$ = $\frac{2} {6}$ = Rs. $\frac{1}{3}$

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

= $\left ( \frac{3}{2 \times 3} \times 100 \right )$

= $\frac{100}{2}$

= 50%

Q11: 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

Sol:

(d) Rs. 600

SP of the chair = Rs. 720

Gain% = 20

CP = $\left [\frac{100}{100 + Profit \%} \times SP \right ]$

= $\left [ \frac{100}{120} \times 720 \right ]$

= $\frac{7200}{12}$

= Rs. 600

Q12: 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

Sol:

(c) Rs. 700

SP of a stool = Rs. 630

Loss% = 10

CP = $\left [ \frac{100}{100 – Loss \%} \times SP \right ]$

= $\left [ \frac{100}{100 – 10} \times 630 \right ]$

= $\frac{100}{90} \times 630$

= Rs. 700

#### Practise This Question

The additive inverse of the rational number ab is - ba.