A dishonest fruit-seller sells fruits at 20% profit but he uses 950 gm weight in place of 1 kg. What is the profit per cent?

Correct — A. Fix his cost at ₹1 per gram, so one true kilogram of fruit costs him ₹1,000.

He hands over only 950 g, so what he parts with cost him ₹950.
He charges the 1 kg price at 20% profit = 1000 × 1.2 = ₹1,200.
Profit = 1200 − 950 = ₹250.

Profit % = 250⁄950 × 100 = 25000⁄950 = 500⁄19 % ≈ 26.32% → option (a).

Why the others are wrong

• (b)
  500⁄32 % is about 15.6%, less than the 20% he already makes on an honest kilogram. Short-weighing can only push the margin above 20%, never below it.
• (c)
  700⁄19 % ≈ 36.8% is this same 950 g calculation run with a 30% mark-up: 130 × 1000⁄950 − 100 = 700⁄19. The stem announces 20%.
• (d)
  500⁄17 % ≈ 29.4% keeps the right ₹250 profit but divides it by 850. The denominator is his own cost, ₹950, which is what he actually gives away.

Two gains are stacked here and the question asks for the combined one.

The first is the honest 20% he adds to his price. The second comes from the short weight — the customer pays for 1,000 g and carries away 950 g, so 50 g of stock never leaves the shop.

The safe method is to fix a unit cost, price one nominal kilogram, then compare his takings with what he actually parted with. Nothing has to be memorised.

Key facts

• A false-weight gain is computed on what the seller gives up, not on the weight the customer pays for.
• With a mark-up of p% and w grams sold as 1,000 g, the gain is (100 + p) × 1000⁄w − 100.
• Here that is 120 × 1000⁄950 − 100 = 500⁄19 %, about 26.32%.
• Using a lighter weight can only raise the seller's percentage gain above the honest mark-up.

Common traps

• Adding the 20% mark-up to the 5% short weight and answering 25%
• Dividing the ₹250 profit by 1,000 rather than by the ₹950 the seller actually spends
• Calling the short weight a 5% gain because 50 g is 5% of 1,000 g, when it is 50⁄950 of his cost

No directly related past PYQ was found.