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: Work with the selling price per orange directly.
When 32 oranges are sold for Rs. 1,000, the selling price per orange is $\frac{1000}{32} = 31.25$.
This price represents a 40% loss, so it equals 60% of the true cost price per orange.

Step 2: Recover the cost price per orange from this single value.
\[ CP = \frac{31.25}{0.6} = 52.08 \]
This matches what a total-cost calculation would give, confirming the per-unit approach is consistent.

Step 3: Find the required selling price per orange for a 20% profit.
A 20% profit means the new selling price is 1.2 times the cost price.
\[ SP_{\text{new}} = 52.08 \times 1.2 = 62.5 \]

Step 4: Divide the total money by the new price per orange.
Since each orange now sells for Rs. 62.5, the number of oranges that together make Rs. 1,000 is:
\[ x = \frac{1000}{62.5} = 16 \]

Final Answer:
Working through the price per single orange also confirms that 16 oranges must be sold for Rs. 1,000 to earn a 20% profit. \[ \boxed{16} \]