Profit and Loss — A merchant usually earns a 25% profit. In one consignment, 25% of the goods were abducted (lost permanently). To compensate, he increased the selling price of the remaining stock by 20% over his usual selling price. What is his overall percentage result on the original cost: profit or loss?

Introduction / Context:
This question mixes a stock loss (25% of goods lost before sale) with a price hike on the remaining goods (selling price increased by 20% over the usual selling price). It tests weighted revenue reasoning under unusual shocks to inventory.

Given Data / Assumptions:

• Normal profit rate = 25% (so usual SP per unit = 1.25 * CP per unit).
• Physical loss: 25% of the consignment is lost and cannot be sold.
• The remaining 75% is sold at 20% above the usual SP (i.e., 1.20 * usual SP).
• All units have the same CP per unit.

Concept / Approach:
Work with convenient round numbers. Let CP per unit = 100 and quantity = 100 units. Then total CP = 100 * 100 = 10000. Usual SP per unit = 125. After the 25% shrinkage, 75 units remain. New SP per unit = 1.20 * 125 = 150. Compute total revenue and compare with total CP to find the overall percentage gain or loss.

Step-by-Step Solution:

Verification / Alternative check:
Using any other unit CP (say 1) scales both cost and revenue proportionally; the net percentage remains 12.5% profit.

Why Other Options Are Wrong:
10% loss, 12.5% loss, and 11.11% loss contradict the computed positive margin; 10% profit understates the true gain of 12.5%.

Common Pitfalls:
Applying the 20% increase to the cost instead of the usual selling price, or forgetting that only 75% of the stock is sold and thus revenue must be computed on fewer units.

Final Answer:
12.5% profit