A sells a bicycle to B at a 20% profit, and B sells it to C at a 25% profit. If C pays ₹1,500, what did A pay for it?
₹1,000. Each sale multiplies the price: CP of A x 1.2 x 1.25 = 1,500, so A's cost = 1,500 / 1.5 = ₹1,000.
Explain it simply
Each step in the chain is a multiplier on the previous price, like a chain of resellers on a marketplace each adding their margin. Two successive profits of 20% and 25% are not a 45% total; they multiply to 1.2 x 1.25 = 1.5, a 50% total. To go backwards, divide by the combined multiplier.
Example
Question: A to B at 20% profit, B to C at 25% profit, C pays ₹1,500. Find A's cost.
- Combined multiplier = 1.20 x 1.25 = 1.5.
- A's cost x 1.5 = 1,500.
- A's cost = ₹1,000.
Forward check: A sells to B at 1,000 x 1.2 = ₹1,200. B sells to C at 1,200 x 1.25 = ₹1,500. Correct.
If one of the steps is a loss, use a multiplier below 1. For example, a 20% profit then a 10% loss: 1.2 x 0.9 = 1.08, a net 8% profit.
console.log(1500 / (1.2 * 1.25)); // Output: 1000
console.log(Math.round((1.2 * 0.9 - 1) * 100)); // Output: 8What to say in the interview
"Each sale multiplies the price, so the chain gives 1.2 times 1.25, which is 1.5. Dividing 1,500 by 1.5 gives A's cost of 1,000, and a forward check confirms it."
Common mistakes
- Adding the percentages to get 45%.
- Taking 25% off ₹1,500 and then 20% off the result; reversing a 25% rise needs division by 1.25, not a 25% cut.