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