Practice MCQ Questions and Answer on Profit and Loss

21.

A house and a shop were sold for Rs. 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale resulted into 20% profit. The entire transaction resulted in -

(A) No loss, no gain
(B) Loss of Rs. $\frac{1}{12}$ lakh
(C) Loss of Rs. $\frac{1}{18}$ lakh
(D) Gain of Rs. $\frac{1}{24}$ lakh

Solution: $\begin{aligned} Total S .P . = Rs . 2 lakh \\ C .P . of house \\ = Rs . (\frac{100}{80} \times 1) lakh \\ = Rs . \frac{5}{4} lakh \\ C .P .of shop \\ = Rs . (\frac{100}{120} \times 1) lakh \\ = Rs . \frac{5}{6} lakh \\ Total C .P . \\ = Rs . (\frac{5}{4} + \frac{5}{6}) lakh \\ = Rs . \frac{25}{12} lakh \\ ∴ Loss \\ = Rs . (\frac{25}{12} - 2) lakh \\ = Rs . \frac{1}{12} lakh \end{aligned}$

22.

Nikita bought 30 kg of wheat at the rate of Rs. 9.50 per kg and 40 kg of wheat at the rate of Rs. 8.50 per kg and mixed them. She sold the mixture at the rate of Rs. 8.90 per kg. Her total profit or loss in the transaction was -

(A) Rs. 2 loss
(B) Rs. 2 profit
(C) Rs. 7 loss
(D) Rs. 7 profit

23.

By selling some goods at Rs. 31, a salesman loses 7% on his output. Find the percentage profit of loss, when he sells the same at Rs. 35 = ?

(A) Loss 7%
(B) Profit 5%
(C) Loss 5%
(D) Profit 7%

Solution: Selling price of goods = Rs. 31 Cost price of goods $\begin{aligned} = 31 \times \frac{100}{93} \\ = Rs . \frac{100}{3} \\ Profit % \\ = \frac{35 - \frac{100}{3}}{\frac{100}{3}} \times 100 \\ = \frac{\frac{5}{3}}{\frac{100}{3}} \times 100 \\ = 5 % \end{aligned}$

24.

A dishonest dealer defrauds to the extent of x% in buying as well as selling is goods by using faulty weight. What will be the gain percent on his outlay?

(A) $2 x %$
(B) $(\frac{10}{x} + x^{2}) %$
(C) $(2 x + \frac{x^{2}}{100}) %$
(D) $(x + \frac{x^{2}}{100}) %$

Solution: $\begin{aligned} Total profit \\ = x + x + \frac{x \times x}{100} \\ = (2 x + \frac{x^{2}}{100}) % \end{aligned}$

25.

A faulty weighing machine reads 1 kg when 900 gm is actually weighted on it. The shopkeeper marked the price of his goods by 10%, but unfortunately he was caught by the metrology department and then they ordered him to repair his weighing machine and gave punishment to sell the goods at 10% discount on cost price for a month. If each customer is now paying Rs. 20 for 1 kg, then before the raid . . . . . . . . amount they have paid for the same quantity. (Rounded off to two places of decimal)

(A) Rs. 27.16
(B) Rs. 27.04
(C) Rs. 28.05
(D) Rs. 28.15

Solution: After getting caught = as a punishment giving 10% discount on cost price for every 1 kg and customer is paying Rs. 20 for 1 kg. Therefore, Actual cost price (for customer) = $= \frac{20}{0.9} = \frac{200}{9}$ But shopkeeper before raid was selling at marked price which is 10% more than cost price $= 1.1 \times \frac{200}{9} = \frac{220}{9}$ But this amount was before raid paid for 900 gm So, actual amount paid for 1000 gm before raid $= \frac{\frac{220}{9}}{900} \times 1000 = Rs . 27.16$

26.

A watch is sold at a profit of 20%. If both the cost price and the selling price of the watch are decreased by Rs. 100, the profit would be 5% more. Original cost price of the watch is -

(A) Rs. 450
(B) Rs. 500
(C) Rs. 550
(D) Rs. 600

Solution: $\begin{aligned} Let C .P . be Rs . x \\ Profit = 20 % \\ S .P . = 120 % of Rs . x \\ = Rs . \frac{6 x}{5} \\ New C .P . = Rs . (x - 100) \\ New S .P . = Rs . (\frac{6 x}{5} - 100) \end{aligned}$ $\begin{aligned} Profit = \\ Rs . [(\frac{6 x}{5} - 100) - (x - 100)] \\ = Rs . \frac{x}{5} \\ ∴ \frac{x}{5} \times \frac{1}{(x - 100)} \times 100 = 25 \\ \Rightarrow 20 x = 25 (x - 100) \\ \Rightarrow 5 x = 2500 \\ \Rightarrow x = 500 \end{aligned}$

27.

A vegetable vendor sold 1 kg of potatoes for Rs. 25 and earned 25% profit. In the evening, he started selling potatoes with only 10% profit. At what cost (in Rs.) per kg did he sell the potatoes in the evening?

(A) 21
(B) 20
(C) 24
(D) 22

Solution: Selling price of potatoes = 25 $\begin{matrix} \begin{matrix} Cost price & Selling price \\ \begin{matrix} 4 \\ ↓ \times 5 \\ 20 \end{matrix} & \begin{matrix} 5 \\ ↓ \times 5 \\ 25 \end{matrix} \end{matrix} \\ Profit % = 10 % = \frac{1}{10} \\ \begin{matrix} Cost price & Selling price \\ \begin{matrix} 10 \\ ↓ \times 2 \\ 20 \end{matrix} & \begin{matrix} 11 \\ ↓ \times 2 \\ 22 \end{matrix} \end{matrix} \end{matrix}$ Selling price of potatoes in evening = Rs. 22

28.

Abhi bought two articles for Rs. 624. He sold one at a loss of 14% and the other at a profit of 14%. If the selling price of both the articles is equal. Then the difference between their cost prices (in Rs.) is:

(A) 89.64
(B) 87.36
(C) 89.68
(D) 88.84

Solution: $\begin{matrix} I & II \\ Cost Price \to & 50_{\times 57} & 50_{43} \\ Profit/Loss \to & - 7 & + 7 \\ Sale Price \to & 43_{\times 51} & 57_{\times 43} \end{matrix}$ Cost price = 50(57 + 43) = 5000 unit → 624 = 1 unit → $\frac{624}{5000}$ Difference of Cost price $= \frac{(50 \times 14) \times 624}{5000} = 87.36$

29.

Two article are sold for Rs. 5,104 each. On one, the seller gains 16% and on the other, he loses 12%. What is his overall gain percent, nearest to two decimal places?

(A) 0.08%
(B) 0.12%
(C) 0.14%
(D) 0.10%

Solution: $\begin{matrix} + 16 % & - 12 % \\ I & II \\ Cost Price & 25_{\times 22} & 25_{\times 29} \\ Profit/Loss & 4_{\times 22} & - 3_{\times 29} \\ Sale Price & 29_{\times 22} & 22_{\times 29} \end{matrix}$ Cost Price = 25(29 + 22) = 25 × 51 Profit/Loss = 88 - 87 = +1 Profit % $= \frac{1}{25 \times 51} \times 100 = 0.08 %$

30.

A dealer sold an article at 6% loss. Had he sold it for Rs. 64 more, he would have made a profit of 10%. Then the cost of the article is = ?

(A) Rs. 400
(B) Rs. 200
(C) Rs. 164
(D) Rs. 464

Solution: Let the cost price of the article = Rs. 100x Loss% = 6% $\begin{aligned} SP = 100 x \times \frac{94}{100} = Rs . 94 x \\ If SP is Rs . 64 more, \\ \Rightarrow New SP = Rs . (94 x + 64) \\ \Rightarrow Profit % \\ \frac{(94 x + 64) - 100 x}{100 x} \times 100 = 10 \\ \Rightarrow 64 - 6 x = 10 x \\ \Rightarrow 10 x + 6 x = 64 \\ \Rightarrow 16 x = 64 \\ \Rightarrow x = \frac{64}{16} \\ ∴ x = 4 \\ ∴ Cost Price = 100 \times 4 \\ = Rs . 400 \end{aligned}$

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Practice MCQ Questions and Answer on Profit and Loss

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