Profit and Loss — A dealer sells three-fourths of his stock at a 24% gain and the remaining one-fourth at cost price. Find the overall percentage gain on the entire transaction.

Introduction / Context: This is a weighted-average profit question. Only part of the stock earns a profit; the rest sold at cost contributes 0% gain. The final gain% equals the weighted average of segment gains by cost share.

Given Data / Assumptions:

• Fraction sold at 24% profit = 3/4
• Fraction sold at 0% profit = 1/4

Concept / Approach: Overall gain% = (weight_1 * gain_1) + (weight_2 * gain_2), where weights are the cost proportions (assuming uniform cost per unit).

Step-by-Step Solution:

Verification / Alternative check: Consider 4 units at ₹ 100 each: cost = ₹ 400. Sell 3 units at 24% gain ⇒ ₹ 372. One unit at cost ⇒ ₹ 100. Total SP = ₹ 472. Gain = 472 − 400 = ₹ 72 ⇒ 72/400 * 100 = 18%.

Why Other Options Are Wrong: 24% ignores the 0% segment; 15% undercounts the weighted effect; 32% is impossible given only part earns 24%.

Common Pitfalls: Averaging 24% and 0% as (24 + 0)/2 = 12% (incorrect) because the quantities are not equal halves; weights matter.

Final Answer: 18%