Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 7) | Concept of Maths

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: C

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.

A) No Profit No Loss

B) $6.25\%$ Loss

C) $6.25\%$ Gain

D) $5\%$ Loss

Answer

Correct Answer: B

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 = $$\left(\frac{25}{10}\right)^2 = (2.5)^2 = 6.25\%$$

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) $7.6\%$

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: A

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) $250$

B) $300$

C) $350$

D) $400$

Answer

Correct Answer: B

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: C

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: D

Solution: Profit = $11 \times CP$. Total quantity sold = $33$ meters. Gain % = $$\frac{\text{Profit}}{\text{CP of total quantity sold}} \times 100$$ 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) $600$

B) $500$

C) $750$

D) $400$

Answer

Correct Answer: A

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

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: C

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: B

Solution: CP of 2 lemons = $1 \implies$ CP of 1 lemon = $0.5$. SP of 5 lemons = $3 \implies$ 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: D

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

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 7) | Concept of Maths