Two-stage trade: +40% then −20% leads to final price ₹432 A sells a watch to B at a 40% gain, and B sells it to C at a 20% loss. If C pays ₹432, at what price did A originally purchase the watch?

Introduction / Context:
When an item passes through multiple sellers with different percentage changes, reverse the successive multipliers from the final price to recover the original cost price for the first seller.

Given Data / Assumptions:

• C's price (final SP) = ₹432.
• B sells at 20% loss ⇒ B's CP = 432 / 0.80.
• A sells to B at 40% gain ⇒ A's CP = (B's CP) / 1.40.

Concept / Approach:
Use inverse multipliers step by step: divide by (1 − loss%) and then divide by (1 + gain%).

Step-by-Step Solution:
B's CP = 432 / 0.80 = ₹540.A's CP = 540 / 1.40 = ₹385.714... ≈ ₹385.71.

Verification / Alternative check:
Forward check: A's CP 385.714... ⇒ A's SP at +40% = 540; B sells at −20% ⇒ 540 * 0.80 = 432 (matches).

Why Other Options Are Wrong:
₹216 and ₹250 are too low; ₹550 is too high; ₹300 does not satisfy the forward multipliers.

Common Pitfalls:
Subtracting percentages arithmetically or reversing the order of undoing gains and losses.

Final Answer:
₹ 385.71