A fruit seller sells apples at a loss of 5% on the cost price but uses a weight that is 20% less than the actual weight. Find his total profit percentage.

Correct — D. Take the cost of 1 kg as ₹100.

Selling price: a 5% loss on the 1 kg charged → ₹95
Weight actually handed over: 20% less than 1 kg → 800 g
His cost for 800 g: 0.8 × ₹100 = ₹80

Profit: ₹95 − ₹80 = ₹15
Profit %: 15 ÷ 80 × 100 = 18.75% → option (d)

Why the others are wrong

• (a)
  20.62%. — On goods costing ₹80, a 20.62% profit means selling for about ₹96.50. The 5% loss on cost fixes the price at ₹95, so the profit stops at ₹15.
• (b)
  19.25% — 19.25% of ₹80 is ₹15.40. The seller's actual profit is ₹95 − ₹80 = ₹15, which is 18.75% of his cost, not 19.25%.
• (c)
  16.28% — 16.28% of the ₹80 cost is about ₹13.02, short of the ₹15 the seller actually makes by charging ₹95 for goods that cost him ₹80.

A false weight is a hidden cut in quantity. A weight 20% short hands over 800 g for every 1 kg charged, so the seller pays for only 80% of what he bills.

His gain on quantity is 200 g on every 800 g he pays for: 200⁄800 = 25%, not 20%.

The price effect and the weight effect multiply: 0.95 × 1.25 = 1.1875, a profit of 18.75%.

Key facts

• A weight x% short gives a quantity gain of x⁄(100 − x): here 20⁄80 = 25%.
• Overall factor = price factor × quantity factor: 0.95 × 1.25 = 1.1875.
• Profit % is on the seller's real cost, ₹80 for 800 g, not the ₹100 cost of the claimed kilogram.

Common traps

• Taking the short weight as a 20% gain: 1.2 × 0.95 gives 14%, but the quantity gain is 200⁄800 = 25%.
• Dividing the ₹15 profit by ₹100, the cost of the claimed 1 kg, instead of ₹80, the cost of what he hands over.

No directly related past PYQ was found.