Profit and Loss — A seller makes 10% profit on one-fourth of the quantity sold and incurs 20% loss on the remaining three-fourths. What is the overall average result: profit or loss, and by what percent?

Introduction / Context:
Weighted-average percentage problems require weighting each segment’s margin by its share of the cost/quantity. Here, 1/4 earns +10% and 3/4 earns −20% on comparable bases, so the overall average is easily computed by linear combination.

Given Data / Assumptions:

• Segment 1: 1/4 of quantity at +10%.
• Segment 2: 3/4 of quantity at −20%.
• Uniform cost per unit across all units.

Concept / Approach:
Overall percentage = (1/4)*10% + (3/4)*(−20%). Since costs per unit are identical, weighting by fractions suffices to produce the net percentage result on the whole transaction.

Step-by-Step Solution:

Verification / Alternative check:
Consider 4 identical units with CP = 100 each (total 400). Profit on one = 10 ⇒ SP1 = 110. Loss on three = 3 * 20 = 60 ⇒ SP2 = 3 * 80 = 240. Total SP = 350 ⇒ loss = 50 ⇒ 50/400 * 100 = 12.5%.

Why Other Options Are Wrong:
11.25% loss and 10% loss misweight the segments; the profit options contradict the negative net margin.

Common Pitfalls:
Averaging 10% and −20% without weights, which would be −5% and incorrect because the quantities are not equal halves.

Final Answer:
12.5% loss