Practice | Hashtable

91. If selling price is doubled, the profit triples. Find the profit percent.

A. $66 \frac{2}{3}$

B. 100

C. $105 \frac{1}{3}$

D. 120

Solution:

\begin{aligned} Let C .P . be Rs . x and S .P . be Rs . y \\ Then, 3 (y - x) = (2 y - x) \\ \Rightarrow y = 2 x \\ Profit = R s . (y - x) \\ = R s . (2 x - x) \\ = R s . x \\ ∴ Profit % \\ = (\frac{x}{x} \times 100) % \\ = 100 % \end{aligned}

92. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A. 30%

B. 70%

C. 100%

D. 250%

Discuss

Solution:

Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420
Profit = Rs. (420 - 125) = Rs. 295
∴ Required percentage

\begin{aligned} = (\frac{295}{420} \times 100) % \\ = \frac{1475}{21} % \\ = 70 % (approximately) \end{aligned}

93. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A. 4

B. 7

C. 5

D. 6

Discuss

Solution:

\begin{aligned} C .P . of 6 toffees = R s . 1 \\ S .P . of 6 toffees \\ = 120 % of R s . 1 = R s . \frac{6}{5} \\ For R s . \frac{6}{5}, toffees sold = 6. \\ For R s . 1, toffees sold = 6 \times \frac{5}{6} = 5 \end{aligned}

94. The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

A. Rs. 2000

B. Rs. 2200

C. Rs. 2400

D. Data inadequate

Discuss

Solution:

\begin{aligned} Let C .P . be R s . x \\ Then, \frac{1920 - x}{x} \times 100 = \frac{x - 1280}{x} \times 100 \\ \Rightarrow 1920 - x = x - 1280 \\ \Rightarrow 2 x = 3200 \\ \Rightarrow x = 1600 \\ ∴ Required S .P . = 125 % of R s . 1600 \\ = R s . (\frac{125}{100} \times 1600) = R s . 2000 \end{aligned}

95. A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

A. Rs. 18.20

B. Rs. 70

C. Rs. 72

D. Rs. 88.25

Discuss

Solution:

\begin{aligned} C .P . = R s . (\frac{100}{122.5} \times 392) \\ = R s . (\frac{1000}{1225} \times 392) \\ = R s . 320 \\ ∴ Profit = R s . (392 - 320) \\ = R s . 72 \end{aligned}

96. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

A. Rs. 1090

B. Rs. 1160

C. Rs. 1190

D. Rs. 1202

Discuss

Solution:

\begin{aligned} S .P . = 85 % of R s . 1400 \\ = R s . (\frac{85}{100} \times 1400) \\ = R s . 1190 \end{aligned}

97. Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

A. 3.5

B. 4.5

C. 5.6

D. 6.5

Discuss

Solution:

\begin{aligned} Cost Price of 1 toy \\ = R s . (\frac{375}{12}) = R s . 31.25 \\ Selling Price of 1 toy = R s . 33 \\ So, Gain = R s . (33 - 31.25) = R s . 1.75 \\ ∴ Profit % = (\frac{1.75}{31.25} \times 100) % \\ = \frac{28}{5} % = 5.6 % \end{aligned}