False weights with nominal loss — dealer uses 20% less weight A dishonest dealer sells at a quoted 10% loss on cost price but secretly delivers only 80% of the claimed weight. What is his true profit or loss percentage?

Introduction / Context:
When sellers use short weights, the effective quantity delivered is lower than claimed. Even if a price suggests a loss relative to cost for the full weight, the reduced quantity delivered can flip the outcome to a real profit. We compare revenue per “claimed kg” with the actual cost of the lesser quantity handed over.

Given Data / Assumptions:

• Quoted loss on cost: 10% (i.e., SP for 1 kg = 0.90 * CP per kg).
• Actual delivered weight for 1 kg claimed = 0.80 kg.
• Uniform cost per kg.

Concept / Approach:
Let CP per kg = 100 units. Then SP per claimed kg = 90. Actual cost for delivered 0.80 kg = 0.80 * 100 = 80. True gain% = (Revenue − Actual cost)/Actual cost * 100.

Step-by-Step Solution:
Assume CP per kg = 100.Quoted SP for “1 kg” = 90 (10% loss reference).Actual weight delivered = 0.80 kg ⇒ cost incurred = 80.True profit = 90 − 80 = 10 ⇒ Profit% = 10/80 * 100 = 12.5% gain.

Verification / Alternative check:
Equivalent formula: True factor = (SP factor)/(weight factor) relative to CP; here 0.90/0.80 = 1.125 ⇒ 12.5% gain. Matches the detailed computation.

Why Other Options Are Wrong:
22.5% and 10% gain misapply either the loss or weight factor; the loss options contradict the net > 1 factor of 1.125.

Common Pitfalls:
Applying the 10% to the delivered weight instead of the price, or forgetting to compute profit relative to actual cost (not claimed 1 kg).

Final Answer:
12.5% gain