Reverse a loss scenario to a gain target — oranges count for a fixed sum By selling 32 oranges for ₹30, a man incurs a 25% loss. How many oranges should he sell for ₹24 to make a 20% gain instead?

Introduction / Context:
This question connects two different profit scenarios with fixed-sum selling: first a loss at a known pack-rate, then a desired gain at a new total price. The key is to recover the true cost per orange from the loss case, then set a selling rate to reach the target gain for the new money amount.

Given Data / Assumptions:

• Loss case: 32 oranges sold for ₹30 with 25% loss.
• Target case: Sell for ₹24 with 20% gain.
• Uniform cost per orange; quality unchanged.

Concept / Approach:
From the first case, compute SP per orange, then divide by 0.75 to get CP per orange (since a 25% loss means SP = 0.75 * CP). For the target case, SP per orange must be 1.20 * CP. With total SP fixed at ₹24, the count follows by division.

Step-by-Step Solution:
SP per orange (loss case) = 30 / 32 = ₹0.9375.CP per orange = 0.9375 / 0.75 = ₹1.25.Required SP per orange for 20% gain = 1.20 * 1.25 = ₹1.50.For ₹24 total: number of oranges n = 24 / 1.50 = 16.

Verification / Alternative check:
If 16 are sold for ₹24, SP per orange is ₹1.50; profit per orange is ₹0.25 on cost ₹1.25, which is exactly 20% gain.

Why Other Options Are Wrong:
24, 28, or 32 would result in SP per orange lower than ₹1.50, missing the 20% gain.20 would overshoot the required margin.

Common Pitfalls:
Using 25% and 20% on selling price instead of cost, or scaling counts without first finding the true unit cost.

Final Answer:
16