Profit and Loss – Two close gains with a small price change: A bicycle is sold at a gain of 16%. If it had been sold for Rs 20 more, the gain would have been 20%. What is the cost price of the bicycle?

Introduction / Context:
This is a direct application of the relation between selling price, gain percent, and cost price. A small increase in selling price shifts the gain from 16% to 20%, allowing us to solve for the cost price precisely.

Given Data / Assumptions:

• At 16% gain, SP1 = 1.16 * CP
• At 20% gain, SP2 = 1.20 * CP
• SP2 − SP1 = Rs 20

Concept / Approach:
Use SP2 − SP1 = (1.20 − 1.16) * CP = 0.04 * CP. Equate to Rs 20 and solve CP = 20 / 0.04.

Step-by-Step Solution:
SP2 − SP1 = 0.04 * CP = Rs 20CP = 20 / 0.04 = 500Therefore cost price = Rs 500

Verification / Alternative check:
If CP = 500, then SP1 = 580 (16%) and SP2 = 600 (20%); difference is indeed Rs 20.

Why Other Options Are Wrong:
350, 400, 600, and 450 do not satisfy the 4% of CP equals Rs 20 condition.

Common Pitfalls:
Using 20% of Rs 20 or mixing up the base for percentages; the base must be CP.

Final Answer:
Rs 500