Oranges at loss vs. target gain — convert 'x for a rupee' to per-unit price A man sells 12 oranges for one rupee and incurs a 20% loss. How many oranges should he sell for one rupee to secure a 20% gain instead?

Introduction / Context:
When items are priced as 'x for a rupee', converting to per-unit selling price clarifies profit or loss. Here we know a 20% loss occurs at 12-for-1. We must find the new count per rupee that yields a 20% gain on the true cost per orange.

Given Data / Assumptions:

• Selling price at first: SP1 per orange = Rs 1/12.
• Loss = 20% at SP1 ⇒ SP1 = 0.8 × CP ⇒ CP = SP1/0.8.
• Target gain = 20% ⇒ SP2 = 1.2 × CP.

Concept / Approach:
Compute the actual CP from the initial loss relation, then multiply by 1.2 to get the per-unit SP for 20% gain. Finally invert to get 'k for a rupee'.

Step-by-Step Solution:
CP = (1/12) / 0.8 = 1/9.6 ≈ Rs 0.1041667.Required SP for 20% gain: SP2 = 1.2 × CP = 1.2 × 1/9.6 = 1/8 = Rs 0.125.At Rs 0.125 each, one rupee buys 8 oranges ⇒ answer 8.

Verification / Alternative check:
Check gains: SP2 − CP = 0.125 − 0.1041667 ≈ 0.0208333; divide by CP gives 0.2 = 20% (as required).

Why Other Options Are Wrong:
5 or 6 for a rupee make the per-unit price too high (profit > 20%); 10 or 15 make it too low (profit < 20% or even loss).

Common Pitfalls:
Adding/subtracting percentages to the count 12 instead of applying them to the money-per-orange price, or mixing rupees with paise incorrectly.

Final Answer:
8