From discount and loss to profit at MRP: A businessman sells at a 40% discount on MRP and incurs a 30% loss. If instead he sells at MRP (no discount), what will his profit percentage?

Introduction / Context:
This problem links discounting and loss to infer the ratio of MRP to cost. Once that ratio is known, we can compute the profit if sold at MRP without any discount. It is a neat algebraic manipulation of multiplicative price factors.

Given Data / Assumptions:

• With 40% discount: SP = 0.6M.
• This SP yields a 30% loss: SP = 0.7C.
• M is marked price, C is cost price.

Concept / Approach:
Equate 0.6M = 0.7C ⇒ M/C = 7/6. Selling at M implies SP = M. Profit% at M equals [(M − C)/C] * 100 = [(M/C) − 1] * 100.

Step-by-Step Solution:

Verification / Alternative check:
Let C = 6, then M = 7. Discounted SP = 0.6 * 7 = 4.2; loss% = (6 − 4.2)/6 = 30%. At M, profit% = (7 − 6)/6 = 16 2/3%.

Why Other Options Are Wrong:
10%, 20%, 16 1/3%, 25% are not consistent with M/C = 7/6.

Common Pitfalls:
Treating 40% discount and 30% loss as directly additive/subtractive; always convert to factors and solve.

Final Answer:
16 2/3%