A shopkeeper sold 5⁄8 of his articles at a gain of 20% and the remaining at the cost price. What is his gain percentage in the whole transaction?

Correct — C. The stem is an image. It reads: a shopkeeper sold 5⁄8 of his articles at a gain of 20% and the remaining at the cost price, and asks for his gain percentage in the whole transaction.

Take 8 articles costing ₹1 each, so the total cost price is ₹8.

5 articles at 20% gain: SP = 5 × 1.20 = ₹6
3 articles at cost: SP = ₹3
Total SP = 6 + 3 = ₹9

Gain = 9 − 8 = ₹1 on a cost of ₹8, so 1⁄8 = 12.5% — the value printed as 12½% in option (c).

Shortcut: only 5⁄8 of the stock earns anything, so the overall gain is 20% × 5⁄8 = 12.5%.

Why the others are wrong

• (a)
  Option (a) reads 14½%. Since the whole gain is 20% × (share sold at a profit), 14.5% would need that share to be 29⁄40 of the stock. The paper says 5⁄8, which is 25⁄40.
• (b)
  Option (b) reads 13½%, which would put the total selling price at 8 × 1.135 = ₹9.08. The five profitable articles and three cost-price articles together fetch exactly ₹9.
• (d)
  Option (d) reads 16½%, the largest decoy. It would need 33⁄40 of the articles sold at 20% gain, and no reading of 5⁄8 gets there — the ceiling if every article sold at a gain would be 20%.

Overall profit percentage is always total gain ÷ total cost price, never the average of the separate rates.

Here one part earns 20% and the other earns nothing, so the blended rate is the weighted average 20% × 5⁄8 + 0% × 3⁄8 = 12.5%.

Assuming a cost price of ₹1 per article is legitimate because the answer is a ratio: change the unit cost and both the gain and the cost scale together.

Key facts

• Gain% = (total SP − total CP) ⁄ total CP × 100.
• Goods sold at cost price contribute zero gain but still count in the cost base.
• 20% gain on 5⁄8 of the stock is an overall gain of 12.5%.
• 12.5% is 1⁄8, so an SP of ₹9 against a CP of ₹8 is the whole calculation.

Common traps

• Averaging 20% and 0% to get 10% and ignoring that the shares are 5⁄8 and 3⁄8
• Applying the 20% to the whole stock and answering 20%
• Taking 5⁄8 of 20% of only the profitable part, which double-counts the weighting

No directly related past PYQ was found.