Quoted loss with 30% short weight — find the true outcome A dishonest dealer sells at a quoted 10% loss on cost but delivers only 70% of the correct weight. What is his true profit or loss percentage?

Introduction / Context:
Short weight can turn an apparent loss into a real profit. We compare the revenue per claimed unit (using the quoted price) against the actual cost of the smaller quantity delivered to find the true percentage outcome on cost.

Given Data / Assumptions:

• Quoted price implies 10% loss on CP for 1 kg ⇒ SP per claimed kg = 0.90 * CP per kg.
• Only 70% of the weight is delivered per claimed kg.
• Uniform CP per true kg.

Concept / Approach:
Let CP per true kg = 100. Then revenue per claimed kg = 90. Actual cost incurred (0.70 kg) = 70. True profit% = (Revenue − Cost)/Cost * 100.

Step-by-Step Solution:
Assume CP per kg = 100 ⇒ SP per claimed kg = 90.Actual cost for 0.70 kg = 70.Profit = 90 − 70 = 20.Profit% = 20 / 70 * 100 = 28.571...% = 28 4/7% gain.

Verification / Alternative check:
Factor method: effective multiplier = 0.90 / 0.70 = 1.285714... ⇒ 28 4/7% gain, confirming the result.

Why Other Options Are Wrong:
Loss options contradict factor > 1; 28 3/7% and 16 3/7% do not match 0.90/0.70 exactly; 'no profit, no loss' is not supported.

Common Pitfalls:
Computing percentage on SP instead of cost, or subtracting percentages linearly instead of using the ratio approach.

Final Answer:
28 4/7% gain