Marked price from target profit after a given discount: An article costs ₹800. After allowing a 10% discount on the marked price, a gain of 12.5% is made. Find the marked price.

Introduction / Context:
This is a forward price-setting problem. Starting from cost, impose the desired profit to get the required selling price. Then reverse the known discount to back out the marked price that will produce that selling price when discounted by the stated percentage.

Given Data / Assumptions:

• Cost C = ₹800.
• Desired profit = 12.5% ⇒ Target SP = 1.125 * 800 = ₹900.
• Discount on marked price = 10% ⇒ SP = 0.9 * M.

Concept / Approach:
Since SP = 0.9M and SP must equal ₹900, solve for M = SP / 0.9. This ensures that, after discount, the realized SP corresponds to the target profit.

Step-by-Step Solution:

Verification / Alternative check:
With M = ₹1000, discount 10% ⇒ SP = ₹900; profit = ₹100 on ₹800 = 12.5%.

Why Other Options Are Wrong:
₹1100, ₹1200, ₹1300, ₹900 do not map to a 12.5% profit after a 10% discount.

Common Pitfalls:
Applying discount to cost or applying profit to marked price. Keep the bases distinct.

Final Answer:
₹ 1000