By selling 32 apples for Rs 30, a man loses 25%. How many apples should be sold for Rs 24, to gain 20% in the transaction?

16

The correct answer is Option (4) → 16

Step 1: Find the cost price of 32 apples

Let CP of 32 apples = x.

Given: selling price = Rs 30, loss = 25%

$\text{Loss \%} = \frac{\text{CP − SP}}{\text{CP}} \times 100$

$25 = \frac{x - 30}{x} \times 100$

$0.25x = x - 30 ⟹ x - 0.25x = 30 ⟹ 0.75x = 30$

$x = \frac{30}{0.75} = 40$

Cost price of 32 apples = Rs 40

Step 2: Cost price per apple

$\text{CP per apple} = \frac{40}{32} = 1.25$

Step 3: Find number of apples to sell for Rs 24 to gain 20%

Let number of apples = n

• CP of n apples = $1.25 \times n$
• SP of n apples = Rs 24
• Gain = 20% → SP = 1.2 × CP

$24 = 1.2 \times (1.25 \times n) = 1.5 \, n$

$n = \frac{24}{1.5} = 16$