Question 1

1. A retailer buys a second-hand gadget for 1200 and spends 300 on its repairs. He then marks up the total cost by 20% and offers a discount of 10% to the customer. What is his actual profit percentage?

A) 10%B) 12%C) 8%D) 9.5%

Answer

✓ Correct Answer: Option C

Explanation: Solution: Total Cost Price (CP) = Purchase Price + Repairing Cost $CP = 1200 + 300 = 1500$ Marked Price (MP) = CP + 20% of CP = $1500 \times 1.2 = 1800$ Selling Price (SP) after 10% discount = $1800 \times 0.9 = 1620$ Profit = SP - CP = 1620 - 1500 = 120 Profit Percentage = $$\frac{120}{1500} \times 100 = 8%$$

Question 2

2. A merchant sells two items for 4500 each. On one, he gains 25% and on the other, he loses 25%. Find his net gain or loss percentage.

No Profit No Loss

Question 3

3. A dishonest dealer professes to sell his goods at cost price but uses a weight of 920 grams for a kilogram. What is his gain percentage?

A) 8%B) 8.25%C) 7.6%D) 8.69%

Answer

✓ Correct Answer: Option D

Explanation: Solution: The gain percentage in such cases is given by: $$Profit % = \frac{Error}{True Value - Error} \times 100$$ Error = 1000g - 920g = 80g Gain % = $$\frac{80}{920} \times 100 = \frac{800}{92} \approx 8.695%$$

Question 4

4. If the cost price of 18 articles is equal to the selling price of 15 articles, find the gain percentage.

A) 20%B) 16.66%C) 25%D) 15%

Answer

✓ Correct Answer: Option A

Explanation: Solution: Let the CP of 1 article be x. $18 \times CP = 15 \times SP$ $$\frac{SP}{CP} = \frac{18}{15} = \frac{6}{5}$$ Gain = SP - CP = 6 - 5 = 1 Gain % = $$\frac{1}{5} \times 100 = 20%$$

Question 5

5. A man sold an article at a loss of 10%. If he had sold it for 75 more, he would have gained 15%. Find the cost price of the article.

A) 250B) 300C) 350D) 400

Answer

✓ Correct Answer: Option B

Explanation: Solution: Let CP be 100%. Initial SP = 90%. New SP = 115%. Difference in SP = 115% - 90% = 25%. Given 25% = 75. Therefore, $100% = \frac{75}{25} \times 100 = 300$.

Question 6

6. A dealer marks an article 40% above the cost price and sells it allowing two successive discounts of 20% and 25%. Find the overall loss percentage.

A) 10%B) 12%C) 16%D) 20%

Answer

✓ Correct Answer: Option C

Explanation: Solution: Let CP = 100. Marked Price (MP) = 140. SP after first discount (20%) = $140 \times 0.8 = 112$. SP after second discount (25%) = $112 \times 0.75 = 84$. Loss = 100 - 84 = 16. Loss % = 16%.

Question 7

7. By selling 33 meters of cloth, a person gains an amount equal to the cost price of 11 meters of cloth. What is the gain percentage?

A) 25%B) 50%C) 20%D) 33.33%

Answer

✓ Correct Answer: Option D

Explanation: Solution: Profit = $11 \times CP$. Total quantity sold = 33 meters. Gain % = $$\frac{Profit}{CP of total quantity sold} \times 100$$ Gain % = $$\frac{11 \times CP}{33 \times CP} \times 100 = \frac{1}{3} \times 100 = 33.33%$$

Question 8

8. An item is sold at a profit of 20%. If both the cost price and selling price were reduced by 100, the profit would have been 24%. Find the original cost price.

A) 600B) 500C) 750D) 400

Answer

✓ Correct Answer: Option A

Explanation: Solution: Let original CP = x. Original SP = 1.2x. New CP = x - 100. New SP = 1.2x - 100. New Profit = 24% of New CP. $$1.2x - 100 = (x - 100) \times 1.24$$ $1.2x - 100 = 1.24x - 124$ $$0.04x = 24 ⇒ x = \frac{24}{0.04} = 600$$

Question 9

9. A trader buys two types of rice. Type A at 60/kg and Type B at 80/kg. He mixes them in the ratio 3:2 and sells the mixture at 75/kg. What is his profit percentage?

A) 8.5%B) 12%C) 10.29%D) 9.75%

Answer

✓ Correct Answer: Option C

Explanation: Solution: Let he buys 3kg of Type A and 2kg of Type B. Total CP = $(3 \times 60) + (2 \times 80) = 180 + 160 = 340$. Total Weight = 5 kg. Total SP = $5 \times 75 = 375$. Profit = 375 - 340 = 35. Profit % = $$\frac{35}{340} \times 100 = \frac{350}{34} \approx 10.29%$$

Question 10

10. A fruit seller buys lemons at 2 for 1 and sells them at 5 for 3. What is his gain percentage?

A) 15%B) 20%C) 25%D) 10%

Answer

✓ Correct Answer: Option B

Explanation: Solution: CP of 2 lemons = 1 ⇒ CP of 1 lemon = 0.5. SP of 5 lemons = 3 ⇒ SP of 1 lemon = 3/5 = 0.6. Gain per lemon = 0.6 - 0.5 = 0.1. Gain % = $$\frac{0.1}{0.5} \times 100 = 20%$$

Accepted Answer

✓ Correct Answer: Option B

Explanation: Solution: When two items are sold at the same Selling Price (SP), one at a gain of x% and the other at a loss of x%, there is always an overall loss given by: Loss Percentage = $$\left(\frac{x}{10}\right)^2%$$ Here, x = 25. Loss = $$\left(\frac{25}{10}\right)^2 = (2.5)^2 = 6.25%$$

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 7)

1. A retailer buys a second-hand gadget for 1200 and spends 300 on its repairs. He then marks up the total cost by 20% and offers a discount of 10% to the customer. What is his actual profit percentage?

2. A merchant sells two items for 4500 each. On one, he gains 25% and on the other, he loses 25%. Find his net gain or loss percentage.

3. A dishonest dealer professes to sell his goods at cost price but uses a weight of 920 grams for a kilogram. What is his gain percentage?

4. If the cost price of 18 articles is equal to the selling price of 15 articles, find the gain percentage.

5. A man sold an article at a loss of 10%. If he had sold it for 75 more, he would have gained 15%. Find the cost price of the article.

6. A dealer marks an article 40% above the cost price and sells it allowing two successive discounts of 20% and 25%. Find the overall loss percentage.

7. By selling 33 meters of cloth, a person gains an amount equal to the cost price of 11 meters of cloth. What is the gain percentage?

8. An item is sold at a profit of 20%. If both the cost price and selling price were reduced by 100, the profit would have been 24%. Find the original cost price.

9. A trader buys two types of rice. Type A at 60/kg and Type B at 80/kg. He mixes them in the ratio 3:2 and sells the mixture at 75/kg. What is his profit percentage?

10. A fruit seller buys lemons at 2 for 1 and sells them at 5 for 3. What is his gain percentage?