Two linked sales with loss and gain — recover original cost A man sells a car to a friend at a 10% loss. The friend later sells it for Rs 54,000 and makes a 20% gain. What was the car's original cost price for the first man?

Introduction / Context:We have two consecutive sales: the second seller earns a 20% gain at a known selling price, which lets us recover his cost. That cost equals the first seller's selling price at a 10% loss, which then unveils the first seller's original cost price.

Given Data / Assumptions:

• Second sale: SP2 = 54,000 with 20% gain ⇒ CP2 = 54,000 / 1.20 = 45,000.
• First sale: SP1 = CP2 = 45,000 with 10% loss ⇒ CP1 = 45,000 / 0.90.

Concept / Approach:Reverse percentages successively: first undo the second seller's gain, then undo the first seller's loss to get the original CP.

Step-by-Step Solution:CP2 = 45,000 (friend's cost).CP1 = 45,000 / 0.90 = 50,000.

Verification / Alternative check:Forward check: 50,000 at 10% loss → 45,000; then 45,000 at 20% gain → 54,000 (matches the given).

Why Other Options Are Wrong:25,000 and 37,500 are too low; 60,000 is too high; 45,000 is the friend's cost, not the original CP.

Common Pitfalls:Applying 10% to 54,000 or mixing up whose gain/loss is applied at which step.

Final Answer:Rs 50,000