Profit and Loss – Adjust quantity to switch from loss to profit: By selling 45 oranges for Rs 40, a man incurs a 20% loss. How many oranges should he sell for Rs 24 to earn a 20% profit?

Introduction / Context:
This problem involves converting between price-per-piece at a known loss and price-per-piece at a target profit. Find the true cost per orange first, then determine the number of oranges needed at the new target selling price to achieve the desired gain.

Given Data / Assumptions:

• Sells 45 oranges for Rs 40 at 20% loss
• Wants 20% profit in the second case
• Second total selling price = Rs 24

Concept / Approach:
From loss information, SP per orange = 40/45. Since loss = 20%, SP = 0.80 * CP ⇒ CP per orange = SP / 0.80. For 20% gain, SP per orange must be 1.20 * CP. Use the total SP to get the number of oranges.

Step-by-Step Solution:
SP1 per orange = 40/45 = 8/9CP per orange = (8/9) / 0.80 = (8/9) * (5/4) = 10/9Target SP per orange = 1.20 * 10/9 = 4/3Number needed for Rs 24: n * (4/3) = 24 ⇒ n = 24 * 3/4 = 18

Verification / Alternative check:
At n = 18, total SP = 24; CP total = 18 * (10/9) = 20; profit = 4 ⇒ 20%.

Why Other Options Are Wrong:
16, 20, and 22 do not satisfy the pricing; 24 would overshoot profit target.

Common Pitfalls:
Using 20% of selling price instead of cost price when converting between loss and profit cases.

Final Answer:
18