Raj sells a lamp for Rs.450 and bears a loss of 20%. To earn a profit of 20%,…

The percentage profit or loss on any transaction is always calculated on the Cost Price (CP), never on the Selling Price. So if CP is fixed, then SP = CP × (1 − loss%) during a loss sale, and SP = CP × (1 + profit%) when a profit is desired — the same CP anchors both selling prices.

1. Let CP be the cost price of the lamp.

2. Raj sells it for Rs.450 at a 20% loss, so 450 = CP × (1 − 0.20) = CP × 0.80, giving CP = 450 ÷ 0.80 = Rs.562.50.

3. To earn a 20% profit on the same CP, the new selling price = CP × (1 + 0.20) = 562.50 × 1.20 = Rs.675.

Cross-check:

• 562.50 × 0.80 = 450, which matches the original loss sale exactly.

• (675 − 562.50) ÷ 562.50 = 0.20, confirming a clean 20% profit on the same cost price.

So Raj must sell the lamp for Rs.675 to earn a 20% profit.