Profit and Loss – Short weight with apparent selling loss: A dishonest dealer sells articles at a 10% loss on cost but uses a weight of 16 g instead of the correct 18 g. What is his actual net profit or loss percentage?

Introduction / Context:
A classic cheating-weights problem: the trader appears to suffer a price loss but delivers less quantity than stated. The short weight increases his effective price per true gram. We must combine the price factor (−10%) with the quantity factor (short measurement) to find the real outcome.

Given Data / Assumptions:

• Advertised loss on price = 10% ⇒ factor = 0.90
• Weight used = 16 g for a labeled 18 g ⇒ customer receives 16 g while paying for 18 g

Concept / Approach:
Let the cost for 18 g be C. Then selling revenue per labeled 18 g is 0.90C but only 16 g are delivered. Revenue per true gram = (0.90C) / 16. Cost per true gram = C / 18. The overall multiplier relative to cost is (0.90C/16) / (C/18) = 0.90 * 18 / 16 = 1.0125.

Step-by-Step Solution:
Overall factor = 1.0125Net profit% = (1.0125 − 1) * 100 = 1.25% = 1 1/4% gain

Verification / Alternative check:
Think per true 18 g: at 10% price loss revenue would be 0.90C, but giving only 16 g while charging for 18 g scales revenue by 18/16 = 1.125, producing 1.0125 overall.

Why Other Options Are Wrong:
2 3/4% and 5 1/4% gains are too high. The loss choices contradict the net factor exceeding 1.00.

Common Pitfalls:
Adding −10% and +12.5% to claim +2.5% without converting to multiplicative factors; always multiply the effects.

Final Answer:
1 1/4% gain