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) $\2,850B) $\3,000C) $\3,125D) $\2,960

Answer

✓ Correct Answer: Option C

Explanation: 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, so0.152x = 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 g for every 1 kg while purchasing from the wholesaler, and another faulty scale that reads 900 g for every 1 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.

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: Option D

Explanation: Solution: $15 \times CP = 12 \times SP ⇒ \frac{SP}{CP} = \frac{15}{12} = \frac{5}{4}$. Profit (P) per lens = 5 - 4 = 1 unit. Profit % = $\frac{1}{4} \times 100 = 25%$. Given: Discount on 8 lenses = Profit on 5 lenses. $8 \times D = 5 \times P ⇒ D = \frac{5}{8} \times 1 = 0.625$. 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) $\960B) $\1,000C) $\880D) $\1,050

Answer

✓ Correct Answer: Option A

Explanation: 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) $\880B) $\920C) $\900D) $\950

Answer

✓ Correct Answer: Option B

Explanation: 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: Option C

Explanation: 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) $\600B) $\580C) $\620D) $\550

Answer

✓ Correct Answer: Option A

Explanation: 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 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 kgB) 500 kgC) 550 kgD) 600 kg

Answer

✓ Correct Answer: Option D

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

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: Option B

Explanation: Solution: Let original CP = x, SP = y. Original Profit P = y - x. New SP = 2y. New Profit P' = 2y - x. Given P' = 3P ⇒ 2y - x = 3(y - x). 2y - x = 3y - 3x ⇒ 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 $\80B) No gain, no lossC) Loss of $\80D) Loss of $\40

Answer

✓ Correct Answer: Option C

Explanation: 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: Option A

Explanation: Solution: Let CP of 1 m cloth = x. CP of 33m = 33x. Profit = CP of 11m = 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 kg more for $\160. What is the reduced price per kg?

A) $\10B) $\12C) $\8D) $\9

Answer

✓ Correct Answer: Option C

Explanation: Solution: Total money = 160. 20% of 160 = 32. This $\32 savings allows buying 4 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 losesD) Loses 2.5%

Answer

✓ Correct Answer: Option B

Explanation: 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 g instead of 1 kg. His total profit percentage is:

A) 25%B) 27%C) 32%D) 30%

Answer

✓ Correct Answer: Option D

Explanation: 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) $\7,500,000B) $\7,875,000C) $\7,250,000D) $\8,000,000

Answer

✓ Correct Answer: Option B

Explanation: 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: Option A

Explanation: 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: Option C

Explanation: 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) 10B) 12C) 15D) 8

Answer

✓ Correct Answer: Option B

Explanation: Solution: Total CP = 600. Total Profit = 198 ⇒ 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) $\130.50B) $\135.20C) $\144.00D) $\140.25

Answer

✓ Correct Answer: Option D

Explanation: 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) $\300B) $\350C) $\320D) $\340

Answer

✓ Correct Answer: Option C

Explanation: 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). $0.75 \times MP = 240 ⇒ MP = \frac{240}{0.75} = 320$.

Accepted Answer

✓ Correct Answer: Option B

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

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 1)

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.

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?

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

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.

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?

8. A merchant has 1000 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:

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

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.

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

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

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:

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 g instead of 1 kg. His total profit percentage is:

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?

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

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?

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?

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%?

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.