Partial profit on a fraction of stock — real overall gain A shopkeeper sells 3/4 of his articles at a 20% gain and the remaining 1/4 at cost price. What is his overall percentage gain?

Introduction / Context:
Overall profit across mixed outcomes is the weighted average of the component percentage outcomes, weighted by the cost (or quantity when unit costs are uniform). Here, 3/4 of the stock yields +20% while 1/4 yields 0%.

Given Data / Assumptions:

• Fraction 1: 3/4 at +20%.
• Fraction 2: 1/4 at 0% (sold at CP).
• Uniform unit cost across all articles.

Concept / Approach:
Weighted average gain% = (0.75 × 20%) + (0.25 × 0%) = 15% overall.

Step-by-Step Solution:
Compute: 0.75 × 20 = 15.Add: 15 + 0 = 15%.

Verification / Alternative check:
Assume total CP = 100. Portion 1 CP = 75 ⇒ SP = 75 × 1.20 = 90. Portion 2 CP = 25 ⇒ SP = 25. Total SP = 115 ⇒ Profit = 15% (confirms).

Why Other Options Are Wrong:
10% underestimates; 20% and 25% ignore the zero-gain portion; 12% is not the weighted result.

Common Pitfalls:
Taking a simple average of 20% and 0% (=10%) without weighting by the 3:1 split.

Final Answer:
15%