Profit and Loss – Mixed gains to hit a target overall margin: A dealer buys 80 cricket bats at ₹ 50 each (total cost ₹ 4000). He sells 20 bats at a 5% gain. What gain percentage must he earn on the remaining 60 bats so that his overall gain on the entire lot is 10%?

Introduction / Context:Here we mix two groups of items with different realized gains. The dealer wants a 10% gain overall, but he has already sold a portion at 5% gain. We must set the gain on the remaining portion so that the total selling price meets the target revenue for 10% overall profit. This requires careful separation of costs and proceeds by group.

Given Data / Assumptions:

• Total bats = 80, cost per bat = ₹ 50
• Total cost = 80 * 50 = ₹ 4000
• Sold 20 bats at 5% gain
• Target overall gain = 10%

Concept / Approach:Compute revenue from the first 20 bats, then find the total revenue required for 10% overall gain. The difference must come from the remaining 60 bats. Convert that into a per-bat selling price and then into a percentage gain on their cost price (₹ 50 each).

Step-by-Step Solution:Revenue from first 20 = 20 * 50 * 1.05 = ₹ 1050Total revenue needed = 4000 * 1.10 = ₹ 4400Revenue needed from remaining 60 = 4400 − 1050 = ₹ 3350Per-bat SP for remaining = 3350 / 60 ≈ ₹ 55.8333Gain% on remaining = (55.8333 − 50) / 50 * 100 ≈ 11.666...% = 11 2/3%

Verification / Alternative check:Total of ₹ 1050 + ₹ 3350 = ₹ 4400, which is exactly 10% above the total cost of ₹ 4000. Hence the overall target is achieved.

Why Other Options Are Wrong:12 1/2% and 9% are close but do not produce the exact total revenue. 6% and 8% are too low and lead to underachievement of the 10% overall target.

Common Pitfalls:Using a simple average of 5% and target 10% instead of weighting by quantities and converting back to per-bat selling price.

Final Answer:11 2/3%