Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 1) | Concept of Maths

Question 1

1. A retailer marks up the price of a high-end graphics card by $60\%$. He then offers two successive discounts of $20\%$ and $10\%$. If the local government imposes an $18\%$ tax on the final selling price, and the retailer still makes a net profit of $\$475$ (excluding tax), what was the original cost price of the card?

A) $\$2,850$

B) $\$3,000$

C) $\$3,125$

D) $\$2,960$

Answer

Correct Answer: C

Solution: Let Cost Price (CP) = $x$. Marked Price (MP) = $x \times 1.60 = 1.6x$. Price after first discount = $1.6x \times 0.80 = 1.28x$. Price after second discount (Final SP before tax) = $1.28x \times 0.90 = 1.152x$. Profit = $SP - CP = 1.152x - x = 0.152x$. Given Profit = $\$475$, so $0.152x = 475$. $x = \frac{475}{0.152} = 3125$. The original cost price is $\$3,125$.

Question 2

2. A dishonest trader uses a faulty scale that reads $1100\text{ g}$ for every $1\text{ kg}$ while purchasing from the wholesaler, and another faulty scale that reads $900\text{ g}$ for every $1\text{ kg}$ while selling to customers. If he offers a nominal discount of $10\%$ on the marked price which is $20\%$ above his cost, find his actual profit percentage.

A) $28.33\%$

B) $32.00\%$

C) $34.44\%$

D) $30.55\%$

Answer

Correct Answer: B

Solution: While Buying: He gets $1100\text{ g}$ for the price of $1000\text{ g}$. Effective CP of $1\text{ g} = \frac{1000}{1100}$ units of money. While Selling: He sells $900\text{ g}$ but charges for $1000\text{ g}$. Nominal SP = $1.20 \times 0.90 = 1.08$ times CP per unit. But he charges this $1.08$ on $1000\text{ g}$ while actually giving $900\text{ g}$. Total money received for $1100\text{ g} = \left(\frac{1100}{900}\right) \times 1.08 \times 1000$. Profit Multiplier = $\left(\frac{1100}{900}\right) \times 1.08 = \frac{11}{9} \times 1.08 = 11 \times 0.12 = 1.32$. Profit percentage = $(1.32 - 1) \times 100 = 32\%$.

Question 3

3. The cost price of $15$ vintage lenses is equal to the selling price of $12$ lenses. The discount offered on $8$ lenses is equal to the profit earned on $5$ lenses. Find the difference between the profit percentage and the discount percentage.

A) $10.5\%$

B) $12.25\%$

C) $15.0\%$

D) $13.89\%$

Answer

Correct Answer: D

Solution: $15 \times CP = 12 \times SP \implies \frac{SP}{CP} = \frac{15}{12} = \frac{5}{4}$. Profit ($P$) per lens = $5 - 4 = 1$ unit. Profit $\%$ = $\frac{1}{4} \times 100 = 25\%$. Given: Discount on $8$ lenses = Profit on $5$ lenses. $8 \times D = 5 \times P \implies D = \frac{5}{8} \times 1 = 0.625$. Marked Price ($MP$) = $SP + D = 5 + 0.625 = 5.625$. Discount $\%$ = $\frac{D}{MP} \times 100 = \frac{0.625}{5.625} \times 100 = \frac{1}{9} \times 100 = 11.11\%$. Difference = $25\% - 11.11\% = 13.89\%$.

Question 4

4. A wholesaler sells a batch of organic honey to a retailer at a profit of $20\%$. The retailer then sells it to a consumer. If the consumer paid $\$1,440$ and the retailer made a profit of $25\%$, what was the cost price for the wholesaler?

A) $\$960$

B) $\$1,000$

C) $\$880$

D) $\$1,050$

Answer

Correct Answer: A

Solution: Let Wholesaler's CP = $W$. Retailer's CP = $1.20W$. Consumer's Price (Retailer's SP) = $1.25 \times (1.20W) = 1.50W$. Given $1.50W = 1440$. $W = \frac{1440}{1.5} = 960$.

Question 5

5. On selling an antique clock for $\$720$, a person loses $10\%$. At what price should he sell it to gain $15\%$?

A) $\$880$

B) $\$920$

C) $\$900$

D) $\$950$

Answer

Correct Answer: B

Solution: $SP_1 = \$720$, Loss $= 10\%$. $CP = \frac{SP_1}{0.90} = \frac{720}{0.9} = 800$. Desired Profit $= 15\%$. $SP_2 = 1.15 \times 800 = 920$.

Question 6

6. A tea merchant mixes two varieties of tea, 'A' costing $\$240$ per kg and 'B' costing $\$360$ per kg, in the ratio $3:2$. If he sells the mixture at $\$345.60$ per kg, find his profit percentage.

A) $15\%$

B) $18\%$

C) $20\%$

D) $22\%$

Answer

Correct Answer: C

Solution: Mean CP = $\frac{(3 \times 240) + (2 \times 360)}{3+2} = \frac{720 + 720}{5} = \frac{1440}{5} = 288$ per kg. $SP = 345.60$ per kg. Profit = $345.60 - 288 = 57.60$. Profit $\%$ = $\frac{57.60}{288} \times 100 = 20\%$.

Question 7

7. A publisher allows a $10\%$ discount on the printed price of a book and still gains $20\%$. If the cost price is $\$450$, what is the printed price?

A) $\$600$

B) $\$580$

C) $\$620$

D) $\$550$

Answer

Correct Answer: A

Solution: Relationship: $\frac{MP}{CP} = \frac{100 + P\%}{100 - D\%}$. $\frac{MP}{450} = \frac{100 + 20}{100 - 10} = \frac{120}{90} = \frac{4}{3}$. $MP = \frac{4}{3} \times 450 = 600$.

Question 8

8. A merchant has $1000\text{ kg}$ of sugar, part of which he sells at $8\%$ profit and the rest at $18\%$ profit. He gains $14\%$ on the whole. The quantity sold at $18\%$ profit is:

A) $400\text{ kg}$

B) $500\text{ kg}$

C) $550\text{ kg}$

D) $600\text{ kg}$

Answer

Correct Answer: D

Solution: Using Alligation: Profit 1: $8\%$, Profit 2: $18\%$, Mean: $14\%$. Ratio = $(18 - 14) : (14 - 8) = 4 : 6 = 2 : 3$. Quantity at $18\%$ = $\frac{3}{2+3} \times 1000 = \frac{3}{5} \times 1000 = 600\text{ kg}$.

Question 9

9. If the selling price is doubled, the profit triples. Find the original profit percentage.

A) $50\%$

B) $100\%$

C) $125\%$

D) $150\%$

Answer

Correct Answer: B

Solution: Let original CP = $x$, SP = $y$. Original Profit $P = y - x$. New SP = $2y$. New Profit $P' = 2y - x$. Given $P' = 3P \implies 2y - x = 3(y - x)$. $2y - x = 3y - 3x \implies 2x = y$. Profit $\%$ = $\frac{y - x}{x} \times 100 = \frac{2x - x}{x} \times 100 = 100\%$.

Question 10

10. A shopkeeper sells two calculators at $\$960$ each. On one he gains $20\%$ and on the other he loses $20\%$. Find his overall gain or loss in the whole transaction.

A) Gain of $\$80$

B) No gain, no loss

C) Loss of $\$80$

D) Loss of $\$40$

Answer

Correct Answer: C

Solution: Total SP = $960 + 960 = 1920$. $CP_1 = \frac{960}{1.2} = 800$. $CP_2 = \frac{960}{0.8} = 1200$. Total CP = $800 + 1200 = 2000$. Loss = $2000 - 1920 = 80$. (Short cut: Always a loss of $\frac{x^2}{100}\%$ where $x=20$. $4\%$ of $2000 = 80$).

Question 11

11. By selling $33$ meters of cloth, a person gains the cost price of $11$ meters. Find the gain percentage.

A) $33.33\%$

B) $25\%$

C) $50\%$

D) $20\%$

Answer

Correct Answer: A

Solution: Let CP of $1\text{ m}$ cloth = $x$. CP of $33\text{ m} = 33x$. Profit = CP of $11\text{ m} = 11x$. Gain $\%$ = $\frac{11x}{33x} \times 100 = 33.33\%$.

Question 12

12. A reduction of $20\%$ in the price of salt enables a purchaser to obtain $4\text{ kg}$ more for $\$160$. What is the reduced price per kg?

A) $\$10$

B) $\$12$

C) $\$8$

D) $\$9$

Answer

Correct Answer: C

Solution: Total money = $160$. $20\%$ of $160 = 32$. This $\$32$ savings allows buying $4\text{ kg}$ more. Reduced Price = $\frac{32}{4} = 8$ per kg.

Question 13

13. A man buys some oranges at $5$ for $\$1$ and an equal number at $4$ for $\$1$. He sells them at $9$ for $\$2$. In this transaction, he:

A) Gains $1.23\%$

B) Loses $1.23\%$

C) Neither gains nor loses

D) Loses $2.5\%$

Answer

Correct Answer: B

Solution: Let he buys $20$ oranges (LCM of $4,5$) of each type. CP of $20$ oranges (type 1) = $4$. CP of $20$ oranges (type 2) = $5$. Total CP for $40$ oranges = $9$. Selling at $9$ for $\$2$ means SP of $1$ orange = $2/9$. Total SP for $40$ oranges = $40 \times \frac{2}{9} = \frac{80}{9} \approx 8.88$. Loss = $9 - 8.88 = 0.11$. Loss $\%$ = $\frac{1/9}{9} \times 100 = \frac{100}{81} \approx 1.23\%$.

Question 14

14. A dealer marks his goods $30\%$ above the cost price and then allows a discount of $10\%$. He also uses a weight of $900\text{ g}$ instead of $1\text{ kg}$. His total profit percentage is:

A) $25\%$

B) $27\%$

C) $32\%$

D) $30\%$

Answer

Correct Answer: D

Solution: Multiplier for Markup & Discount = $1.30 \times 0.90 = 1.17$. Multiplier for Weight Fraud = $\frac{1000}{900} = \frac{10}{9}$. Net Multiplier = $1.17 \times \frac{10}{9} = 0.13 \times 10 = 1.30$. Total Profit $\%$ = $(1.30 - 1) \times 100 = 30\%$.

Question 15

15. A property dealer sells a house for $\$6,000,000$ and incurs a loss of $20\%$. If he wanted to make a profit of $5\%$, at what price should he have sold it?

A) $\$7,500,000$

B) $\$7,875,000$

C) $\$7,250,000$

D) $\$8,000,000$

Answer

Correct Answer: B

Solution: $CP = \frac{6,000,000}{0.80} = 7,500,000$. New SP = $1.05 \times 7,500,000 = 7,875,000$.

Question 16

16. A shopkeeper offers 'Buy 4 Get 1 Free' and an additional $10\%$ discount to a member. What is the effective discount?

A) $28\%$

B) $30\%$

C) $25\%$

D) $32\%$

Answer

Correct Answer: A

Solution: 'Buy 4 Get 1 Free' means $5$ items for the price of $4$. Initial Discount $= \frac{1}{5} = 20\%$. Successive discount formula $= d_1 + d_2 - \frac{d_1 d_2}{100}$. Effective Discount $= 20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28\%$.

Question 17

17. If a merchant buys a chair for $\$1,500$ and spends $\$500$ on repairs and transportation, then sells it for $\$2,500$, what is his profit percentage?

A) $33.33\%$

B) $50\%$

C) $25\%$

D) $40\%$

Answer

Correct Answer: C

Solution: Effective CP = $1500 + 500 = 2000$. SP = $2500$. Profit = $500$. Profit $\%$ = $\frac{500}{2000} \times 100 = 25\%$.

Question 18

18. A fruit seller buys $240$ apples for $\$600$. Some of them are rotten and thrown away. He sells the remaining apples at $\$3.50$ each and makes a profit of $\$198$. How many apples were rotten?

A) $10$

B) $12$

C) $15$

D) $8$

Answer

Correct Answer: B

Solution: Total CP = $600$. Total Profit = $198 \implies$ Total SP = $798$. SP per apple = $3.50$. Number of apples sold = $\frac{798}{3.50} = 228$. Number of rotten apples = $240 - 228 = 12$.

Question 19

19. A person sold an article at a loss of $15\%$. Had he sold it for $\$30.60$ more, he would have gained $9\%$. For how much should he have sold it to gain $10\%$?

A) $\$130.50$

B) $\$135.20$

C) $\$144.00$

D) $\$140.25$

Answer

Correct Answer: D

Solution: Difference in percentage = $9\% - (-15\%) = 24\%$. Given $24\%$ of CP = $30.60$. $CP = \frac{30.60}{0.24} = 127.5$. New SP (to gain $10\%$) = $1.10 \times 127.5 = 140.25$.

Question 20

20. A shopkeeper allows a $25\%$ discount on the marked price and still makes a profit of $20\%$. If he gains $\$40$ on the sale of one article, find the marked price of that article.

A) $\$300$

B) $\$350$

C) $\$320$

D) $\$340$

Answer

Correct Answer: C

Solution: Profit $= 20\%$ of CP $= 40$. $CP = \frac{40}{0.20} = 200$. SP = CP + Profit = $200 + 40 = 240$. Given SP $= 75\%$ of MP (after $25\%$ discount). $0.75 \times MP = 240 \implies MP = \frac{240}{0.75} = 320$.

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 1) | Concept of Maths