Profit and Loss – Short-weight with price gain: A grocer sells rice at a listed profit of 10% but uses weights that are 20% less than the correct weight. What is his overall percentage gain on true quantity delivered?

Introduction / Context:
When a trader both increases price and manipulates quantity using a short weight, the effective gain multiplies the two effects. Price margin and short-measure effects should be converted to factors and then combined.

Given Data / Assumptions:

• Listed price margin (gain) = 10% ⇒ factor 1.10
• Weights 20% less ⇒ customer receives 0.80 of a true kilogram while paying for 1 kg

Concept / Approach:
Short weight increases the effective price by 1 / 0.80 = 1.25 since the buyer pays for 1 kg but gets only 0.80 kg. The overall revenue factor per true kilogram becomes price factor * short-weight factor.

Step-by-Step Solution:
Price factor = 1.10Short-weight factor = 1 / 0.80 = 1.25Overall factor = 1.10 * 1.25 = 1.375Overall gain% = (1.375 − 1) * 100 = 37.5%

Verification / Alternative check:
Assume CP per true kg = 100. Short-weight makes SP per true kg = 100 * 1.10 * 1.25 = 137.5, so gain = 37.5.

Why Other Options Are Wrong:
30% and 35% understate the multiplicative effect; 25% ignores short weight. “None” is false because 37.5% matches the calculation.

Common Pitfalls:
Adding 10% and 20% to get 30% instead of multiplying the factors 1.10 and 1.25.

Final Answer:
37.5%