A grocer professes to sell rice at the cost price, but uses a fake weight of 870 g for 1 kg. Find his profit percentage (correct to two decimal places).

Correct — B. He sells at cost price, so the entire gain hides in the weight: compare what he hands over with what he charges for.

He charges for 1000 g but delivers 870 g.
His real cost for the sale = 870 units, money taken = 1000 units.
Gain = 1000 − 870 = 130 units.

Profit % = gain ÷ cost × 100
= 130⁄870 × 100 = 13000⁄870
= 14.9425…% → 14.94% to two decimal places, option (b).

Why the others are wrong

• (a)
  11.11% — 11.11% is the profit a 900 g weight would give (100⁄900 × 100). The shortfall in this question is 130 g, not 100 g.
• (c)
  15.11% — 15.11% overshoots. The quotient is fixed: 130 ⁄ 870 = 0.1494252…, i.e. 14.94% to two decimal places. A 15.11% gain would need the fake weight to be about 869 g, not 870 g.
• (d)
  18.21% — A 130 g shortfall on an 870 g base caps the gain at 14.94%. Earning 18.21% would need the grocer to hand over only about 846 g per kilogram.

When a trader sells at cost price but under-weighs, the marked price never changes and the profit comes entirely from the short delivery.

The rule: profit % = (true weight − false weight) ⁄ false weight × 100.

The denominator is the false weight, because 870 g is what the seller actually parts with — his real cost for the sale. Putting 1000 in the denominator gives 13%, which is not on the option list.

Key facts

• Profit % on a false weight = (true weight − false weight) ⁄ false weight × 100.
• Here the shortfall is 1000 − 870 = 130 g and the base is 870 g, giving 13000⁄870 = 14.94%.
• Dividing by 1000 instead of 870 returns 13%, which is not among the four options.

Common traps

• Using 1000 g as the denominator, which returns 13% instead of 14.94%
• Rounding 14.9425 up to 15% and then reaching for the nearest-looking option

No directly related past PYQ was found.