A fruit vendor sells 15 kg of apples for ₹750, thereby gaining the cost price of 5 kg of apples. What is his profit percentage?

Correct — B. The gain is the cost of 5 kg, and the outlay is the cost of the 15 kg sold.

Profit% = cost of 5 kg ÷ cost of 15 kg × 100
= 5⁄15 × 100 = 33.33% → option (b)

Check with ₹750: 15 kg sell for the cost of 15 + 5 = 20 kg
Cost per kg: 750 ÷ 20 = ₹37.50
Profit ₹187.50 on a cost of ₹562.50 = 1⁄3

Why the others are wrong

• (a)
  28.65% — 28.65% of the ₹562.50 cost would be about ₹161, but the profit is the cost of 5 kg, 5 × 37.50 = ₹187.50.
• (c)
  26.32% — 26.32% of the ₹562.50 cost would be about ₹148, well short of the ₹187.50 that 5 kg of apples cost.
• (d)
  31.56% — 31.56% of the ₹562.50 cost would be about ₹178, still short of the ₹187.50 profit, which is exactly one third of cost.

When the gain is stated as the cost price of k items, profit and cost are measured in the same unit: kilograms' worth of cost. Profit% is then a ratio of counts, k ÷ items sold × 100.

The vendor sells 15 kg and gains the cost of 5 kg, so profit is 5⁄15 = 1⁄3 of cost. The ₹750 is not needed for the percentage.

Key facts

• If selling n items gains the cost price of k items, profit% = k ÷ n × 100.
• If selling n items loses the cost price of k items, loss% = k ÷ n × 100.
• If selling n items gains the selling price of k items, profit% = k ÷ (n − k) × 100.

Common traps

• Dividing by 20, the kilograms of cost the selling price covers, which gives 5⁄20 = 25%. That is profit as a share of the selling price.
• Treating 'cost price of 5 kg' as 'selling price of 5 kg'. That version gives 5 ÷ (15 − 5) = 50%.

No directly related past PYQ was found.