A fruit seller buys three varieties of mangoes. The first variety is bought at 4 for ₹10, the second at 5 for ₹12, and the third at 2 for ₹5. He mixes them in the ratio 2 : 3 : 1 respectively. If he sells all the mangoes at 3 for ₹7, what is his approximate gain or loss percentage?

Correct — B.
Cost per mango: 10 ÷ 4 = ₹2.50, 12 ÷ 5 = ₹2.40, 5 ÷ 2 = ₹2.50

Take a batch of 2 + 3 + 1 = 6 mangoes
Cost = 2 × 2.50 + 3 × 2.40 + 1 × 2.50 = 5 + 7.2 + 2.5 = ₹14.70
Sale at 3 for ₹7 = 6 for ₹14

Loss = 14.70 − 14 = ₹0.70
Loss % = 0.70 ÷ 14.70 × 100 = 100⁄21 ≈ 4.76%
A loss of 4.76% → option (b).

Why the others are wrong

• (a)
  Profit of 4.76% — Profit gets the direction wrong. A mango costs ₹2.45 on average but sells for 7 ÷ 3 ≈ ₹2.33, below cost. The size 4.76% is right, but it is a loss.
• (c)
  Loss of 6% — A 6% loss is too large. It needs a selling price of 2.45 × 0.94 ≈ ₹2.30 a mango, but 3 for ₹7 is about ₹2.33. The loss is ₹0.70 on ₹14.70, about 4.76%.
• (d)
  Profit of 6% — Profit of 6% is wrong on both counts. The selling price of about ₹2.33 is below the average cost of ₹2.45, so it is a loss, and its size is 4.76%.

For a mixture bought at different rates, first turn every rate into a cost per item, then weight those costs by the mixing ratio.

The first and third varieties both cost ₹2.50, so the batch of 6 is 3 mangoes at ₹2.50 and 3 at ₹2.40: an average cost of ₹2.45.

Profit or loss % is taken on the cost of the batch, ₹14.70, not on the ₹14 received.

Key facts

• Cost per item = price ÷ number bought: 4 for ₹10 is ₹2.50 each.
• Average cost of the mix = (2 × 2.50 + 3 × 2.40 + 1 × 2.50) ÷ 6 = ₹2.45.
• Loss % = (CP − SP) ÷ CP × 100 = 0.70 ÷ 14.70 × 100 ≈ 4.76%.

Common traps

• Averaging the three unit costs without the 2 : 3 : 1 weights, which gives about ₹2.47 and a loss near 5.4%.
• Dividing the ₹0.70 loss by the ₹14 received, which gives 5%.

No directly related past PYQ was found.