Profit and Loss — Two clocks A and B are bought for a total of ₹ 650. Clock A is sold at a 20% profit, clock B at a 25% loss, and both fetch the same selling price. What are the purchase prices of A and B respectively?

Introduction / Context:
When two items sell for the same amount under different percentage outcomes, equating their selling price formulas (in terms of CP) lets us solve for each cost price. The total cost constraint provides the second equation needed.

Given Data / Assumptions:

• CP_A + CP_B = ₹ 650.
• SP_A = 1.20 * CP_A (20% profit).
• SP_B = 0.75 * CP_B (25% loss).
• SP_A = SP_B (equal selling prices).

Concept / Approach:
From equality: 1.20 * CP_A = 0.75 * CP_B ⇒ CP_B = (1.20/0.75) * CP_A = 1.60 * CP_A. Combine with the total cost equation to get both CPs.

Step-by-Step Solution:

Verification / Alternative check:
SP_A = 1.20 * 250 = 300; SP_B = 0.75 * 400 = 300 (equal as required).

Why Other Options Are Wrong:
Other pairs do not satisfy both CP_A + CP_B = 650 and 1.20 * CP_A = 0.75 * CP_B simultaneously.

Common Pitfalls:
Equating profit percentages instead of equating the actual selling prices; forgetting to use the total cost constraint.

Final Answer:
Rs. 250, Rs. 400