Profit and Loss – Infer the (equal) discount rate from final price, then “flip” to equal increases: An item has cost price ₹ 500 and is marked up by 80%, so MP = ₹ 900. It is sold at ₹ 576 after two successive equal discounts. If instead of discounting twice by the same rate, the marked price were increased twice by that same rate, what would be the new profit percentage?

Introduction / Context:
This is a reverse-engineering exercise. Two equal successive discounts bring a marked price down to a known selling price. We first deduce the common discount rate. Then we conceptually “flip” and apply two equal successive increases by the same rate to the marked price, and compute the resulting profit on the original cost.

Given Data / Assumptions:

• CP = ₹ 500
• MP = 1.80 * 500 = ₹ 900
• After two equal discounts: SP = ₹ 576

Concept / Approach:
Let the equal discount rate be d. Then 900 * (1 − d)^2 = 576 ⇒ (1 − d)^2 = 0.64 ⇒ 1 − d = 0.80 ⇒ d = 0.20 (20%). For the hypothetical case, apply two successive +20% increases: 900 * (1.20)^2.

Step-by-Step Solution:
d = 20% from (1 − d)^2 = 576 / 900 = 0.64New SP (two increases) = 900 * 1.44 = ₹ 1296Profit = 1296 − 500 = ₹ 796Profit% = 796 / 500 * 100 = 159.2%

Verification / Alternative check:
Check discount path: two 20% discounts give 900 → 720 → 576, consistent. The increase path reverses the idea and yields the computed profit.

Why Other Options Are Wrong:
59.2% and 109.2% understate the huge two-step increase. 259.2% is too large. “Can’t be determined” is incorrect since d is uniquely found.

Common Pitfalls:
Adding 20% twice to claim 40% up or down; successive percentage changes multiply, not add.

Final Answer:
159.2%