# Profit and Loss Quiz Set 003

### Question 1

A merchant is selling cloth at a profit of 248%. If the cost increases by 16%, but he continues to sell at the same price, then what is the new profit percentage?

A

200%.

B

300%.

C

100%.

D

400%.

Soln.
Ans: a

Let the cost price be CP. Then the SP = CP x (1 + \$248/100\$) = \$348/100\$ × CP. New CP = (1 + \$16/100\$) × CP, which is \$116/100\$ × CP. New Profit% = (SP/CP - 1) × 100, which is \$(({348/100 × CP}/{116/100 × CP}) - 1) × 100)\$, which becomes \$(348 - 116)/116\$ × 100 = 200%.

### Question 2

A profit of 50%, as calculated on the cost price, is made by selling an item for Rs. 18. What is the profit in rupees?

A

Rs. 6.

B

Rs. 7.

C

Rs. 5.

D

Rs. 8.

Soln.
Ans: a

If cost is C, profit is P% and sale is S, then we know that C = \$S/(1 + P/100)\$. So the profit in rupees would be S - C = S - \$S/(1 + P/100)\$, which simplifies to \${S × P}/{100 + P}\$, which is \${18 × 50}/{100 + 50}\$ = Rs. 6.

Shortcut Method: If sale is 150, profit is Rs. 50. So if sale is 18, profit = Rs. \$50/150\$ × 18 = Rs. 6.

### Question 3

4640 items are purchased at a cost of Rs. 10. How many items should be sold for Rs. 10 to make a profit of 16%?

A

4000.

B

4001.

C

3999.

D

4002.

Soln.
Ans: a

The sale price should be 10 × (1 + 16/100), which equals Rs. 1160/100. So, Rs. 1160/100 is the sale price of 4640 items. And, 10 shall be the sale price of \$(4640 × 100/1160)\$ × 10 = 4000 items.

### Question 4

A retailer makes a gain of 30% when he sells the first item for Rs. 780. But he suffers a loss of 25% when he sells the second item for Rs. 375. What is his combined loss or gain?

A

5.

B

6.

C

7.

D

4.

Soln.
Ans: a

The cost of the first item is 780 × \$100/{100 + 30}\$ which is Rs. 600. The cost of the second item is 375 × \$100/{100 - 25}\$ which is Rs. 500. The combined cost is 600 + 500 = Rs. 1100. The combined sale is 780 + 375 = Rs. 1155. The profit percent is 100 × \${1155 - 1100}/1100\$, which is 5%.

### Question 5

A profit of 50%, as calculated on the cost price, is made by selling an item for Rs. 36. What is the profit in rupees?

A

Rs. 12.

B

Rs. 13.

C

Rs. 11.

D

Rs. 14.

Soln.
Ans: a

If cost is C, profit is P% and sale is S, then we know that C = \$S/(1 + P/100)\$. So the profit in rupees would be S - C = S - \$S/(1 + P/100)\$, which simplifies to \${S × P}/{100 + P}\$, which is \${36 × 50}/{100 + 50}\$ = Rs. 12.

Shortcut Method: If sale is 150, profit is Rs. 50. So if sale is 36, profit = Rs. \$50/150\$ × 36 = Rs. 12.