Profit and Loss Quiz Set 004

Question 1

The total cost of two cows is Rs. 230. The owner sells the first cow at a profit of 50%, and the second one at a loss of 20%. If he sells them at the same price, what are the costs of the two cows?

A

Rs. 80 and 150.

B

Rs. 180 and 50.

C

Rs. 30 and 200.

D

Rs. 40 and 190.

Soln.
Ans: a

Let the costs of the cows be C and 230 - C. The sale price is given as same. So (100 + 50) × C = (100 - 20) × (230 - C). Simplifying, we get 150 × C = 80 × (230 - C). Solving for C we get, C = Rs. 80. The cost of the other cow is 230 - 80 = Rs. 150.

Question 2

Goods are purchased at a cost price of Rs. 500 and sold at a loss of 5%. What is the sale price?

A

Rs. 475.

B

Rs. 476.

C

Rs. 474.

D

Rs. 477.

Soln.
Ans: a

The loss in rupees is cost × 5%. Which is \${500 × 5}/100\$ = Rs. 25. So the sale price is cost - loss = 500 - 25 = Rs. 475.

Question 3

A profit of 50%, as calculated on the cost price, is made by selling an item for Rs. 39. What is the profit in rupees?

A

Rs. 13.

B

Rs. 14.

C

Rs. 12.

D

Rs. 15.

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 \${39 × 50}/{100 + 50}\$ = Rs. 13.

Shortcut Method: If sale is 150, profit is Rs. 50. So if sale is 39, profit = Rs. \$50/150\$ × 39 = Rs. 13.

Question 4

A merchant is selling cloth at a profit of 206%. If the cost increases by 2%, 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 + \$206/100\$) = \$306/100\$ × CP. New CP = (1 + \$2/100\$) × CP, which is \$102/100\$ × CP. New Profit% = (SP/CP - 1) × 100, which is \$(({306/100 × CP}/{102/100 × CP}) - 1) × 100)\$, which becomes \$(306 - 102)/102\$ × 100 = 200%.

Question 5

A merchant purchased 37 Kg of wheat at the rate of 6.00 Rs./Kg, and 63 Kg wheat at 8.00 Rs./Kg. At what rate must he sell the mixture to make an overall gain of 5%?

A

7.62.

B

8.62.

C

6.62.

D

9.62.

Soln.
Ans: a

The overall cost is \$37 × 6 + 63 × 8\$ = Rs. 726. Add a profit of 5% to get SP = \$726 + (5 × 726)/100\$ = Rs. 762.3. So the rate = \$762.3/{37 + 63}\$ = \$762.3/100\$ = 7.62. 