A dishonest merchant sells his grocery using weights that are 12% less than the true weights and makes a profit of 10%. Find his total gain percentage.

Correct — D. Option (d) shows 25%.

Take the cost as ₹1 per gram and one claimed sale of 1,000 g.
Goods actually handed over = 1,000 − 12% = 880 g, which cost him ₹880.
He charges for 1,000 g and adds his 10%: 1,000 × 1.10 = ₹1,100.

Gain = 1,100 − 880 = ₹220, on an outlay of ₹880.
220 ⁄ 880 × 100 = 25% → option (d)

Why the others are wrong

• (a)
  Option (a) shows 15%. It credits the short weight with only five percentage points on top of the mark-up. The real lever is the denominator: he spends ₹880, not ₹1,000.
• (b)
  Option (b) shows 20%, which is ₹220 divided by the ₹1,100 he collects instead of the ₹880 he spends. Profit per cent is measured on cost, never on revenue.
• (c)
  Option (c) shows 10%, the honest mark-up on its own. It ignores the 12% short weight, which is the only thing this stem adds to an ordinary profit sum.

A false weight is a cost-side cheat. The seller collects the price of 1,000 g but parts with only 880 g, so his cost falls while his revenue does not.

That makes the two effects multiply rather than add:
gain% = [(100 + mark-up) ⁄ (100 − short%)] × 100 − 100
= (110 ⁄ 88) × 100 − 100 = 25%

The same formula reads 12% as the percentage by which the weight falls short of the true weight, which is exactly how this stem words it.

Key facts

• Profit per cent is always computed on cost price, so shrinking the goods delivered raises it.
• Selling 1,000 g worth of price for 880 g of goods multiplies the honest ratio by 1,000⁄880.
• A 10% mark-up with a 12% short weight gives 25% overall, not the 22% that adding them suggests.

Common traps

• Adding 10% and 12% to reach 22%
• Dividing the gain by the money collected rather than the money spent

No directly related past PYQ was found.