Anand purchased an item and incurred ₹97 in repair expenses. Subsequently, he…

Concept

A percentage profit or loss is always reckoned on the seller’s own cost price, never on the selling price. So SP = CP × (1 + Profit%/100) and SP = CP × (1 − Loss%/100).

Both relations are reversible: dividing a known selling price by the same factor recovers the cost price behind it. In a resale chain, one person’s selling price becomes the next person’s cost price, so the chain can be unwound one step at a time from the last known amount.

A seller’s total cost price means the purchase price plus every additional outlay such as repairs, freight or overheads, because the profit percentage is reckoned on that whole amount.

Application

1. Bharath sold the item for ₹3,133 at a 35% loss, and that loss is reckoned on Bharath’s cost price: ₹3,133 = (Bharath’s CP) × (1 − 35/100) = (Bharath’s CP) × 0.65.

2. Therefore Bharath’s cost price = 3133 ÷ 0.65 = ₹4,820.

3. That ₹4,820 is exactly what Bharath paid Anand, so it is Anand’s selling price.

4. Anand earned a 25% profit on his total cost price: ₹4,820 = (Anand’s total CP) × (1 + 25/100) = (Anand’s total CP) × 1.25.

5. Therefore Anand’s total cost price = 4820 ÷ 1.25 = ₹3,856.

6. The ₹97 spent on repairs is already inside that total, so the price Anand paid for the item by itself was 3856 − 97 = ₹3,759.

Cross-check

Rebuilding the chain forward from the purchase reproduces every amount given in the question:

The final ₹3,133 matches the question, which confirms the chain. Note that the ₹97 is a component of the total cost price, not an extra amount to be added on afterwards, so the total cost price asked for is ₹3,856.