Back-solving cost from marked price and outcome: An article is marked ₹50 and sold with a 20% discount. If the seller’s profit is 25%, find the cost price.

Introduction / Context: This is a one-step back calculation. The marked price gives the selling price after discount; comparing that selling price to an assumed cost with the target profit leads directly to the cost price. Keep track of which percentage applies to which base quantity.

Given Data / Assumptions:

• Marked price M = ₹50.
• Discount = 20% ⇒ Selling price S = 0.8 * 50 = ₹40.
• Profit = 25% on cost ⇒ S = 1.25 * C.

Concept / Approach: With S known, divide by 1.25 to recover cost. This is simply reversing a percentage increase from cost to selling price.

Step-by-Step Solution:

Verification / Alternative check: Selling at ₹40 on a cost of ₹32 gives profit = 8, i.e., 8/32 = 25%, matching the condition.

Why Other Options Are Wrong: ₹40, ₹35, ₹30, ₹28 do not yield a 25% profit when the selling price is ₹40.

Common Pitfalls: Applying the 25% to the marked price instead of the cost; or miscomputing the discounted selling price.

Final Answer: ₹ 32