Profit and Loss — An article is sold at a 25% loss. If the selling price were increased by ₹ 21, the result would be a 10% gain. What is the cost price of the article?

Introduction / Context: This is a classic two-condition percentage problem. One sale gives a loss percentage; a slightly higher selling price flips the outcome to a stated gain percentage. The difference between the two selling prices allows direct recovery of the cost price (CP).

Given Data / Assumptions:

• Sale 1: Loss 25% ⇒ SP1 = 0.75 * CP.
• Sale 2: Gain 10% ⇒ SP2 = 1.10 * CP.
• SP2 − SP1 = ₹ 21.

Concept / Approach: Subtract the two expressions to isolate CP. The 35% spread between −25% and +10% corresponds to the ₹ 21 difference in selling price, yielding CP directly by division.

Step-by-Step Solution:

Verification / Alternative check: SP1 = 0.75 * 60 = 45; SP2 = 1.10 * 60 = 66; difference = 21 (matches).

Why Other Options Are Wrong: 56, 84, and 92 do not satisfy a 35% spread of ₹ 21. 72 yields SP1 = 54 and SP2 = 79.2 (difference 25.2), not 21.

Common Pitfalls: Adding 25% and 10% to SP instead of to CP, or misreading the ₹ 21 increment as percentage instead of an absolute rupee change.

Final Answer: Rs. 60