By selling 12 apples for a rupee, a man loses 20%. How many apples per rupee should he sell to gain 20%?

Introduction:Convert the given selling rate to unit price, infer cost price, then find the new unit price for 20% gain and turn it back into “how many for a rupee.”

Given Data / Assumptions:

• At 12 for Rs 1, loss = 20%
• Goal: gain = 20%

Concept / Approach:Let SP1 per apple = 1/12. With 20% loss, SP1 = 0.8 * CP ⇒ CP = SP1 / 0.8. For 20% gain, SP2 = 1.2 * CP. Then apples per rupee = 1 / SP2.

Step-by-Step Solution:SP1 = 1/12 rupee/appleCP = (1/12) / 0.8 = 1/9.6 rupee/appleSP2 = 1.2 * (1/9.6) = 1/8 rupee/appleApples per rupee = 1 / (1/8) = 8

Verification / Alternative check:Check margins: At 8 for 1 rupee, price is higher than before, aligning with desired gain relative to CP.

Why Other Options Are Wrong:10, 15, 16: Do not satisfy the 20% gain condition given the inferred CP.

Common Pitfalls:Mixing up the base for percent gain/loss; forgetting to convert back to items per rupee.

Final Answer:8