Question

A person incurs a loss of 40% when he sells 32 oranges at Rs. 1,000. In order to make a profit of 20%, how many oranges should he sell at Rs. 1,000?

• A. 12
• B. 14
• C. 16
• D. 18

Hint:

First find the cost price of one orange from the loss situation, then find the selling price per orange needed for the target profit, and divide Rs. 1,000 by that price.

Answer 1

The Correct Option is C

Step 1: Find the total cost price of the 32 oranges.
Selling 32 oranges for Rs. 1,000 results in a 40% loss, which means the selling price is only 60% of the cost price.
\[ CP_{32} = \frac{1000}{0.6} = 1666.67 \]
So the total cost price of 32 oranges is about Rs. 1666.67.

Step 2: Find the cost price of one orange.
\[ CP_{1} = \frac{1666.67}{32} = 52.08 \]
Each orange costs the person about Rs. 52.08.

Step 3: Find the selling price per orange needed for a 20% profit.
A profit of 20% means the selling price is 120% of the cost price.
\[ SP_{1} = 52.08 \times 1.2 = 62.5 \]
So each orange must now be sold for Rs. 62.5 to earn a 20% profit.

Step 4: Find how many oranges make up Rs. 1,000 at this new price.
\[ \text{Number of oranges} = \frac{1000}{62.5} = 16 \]

Final Answer:
He should sell 16 oranges for Rs. 1,000 to make a 20% profit. \[ \boxed{16} \]