A sells a cycle to B at a profit of 20% and B sells it to C at a loss of 25%. If C bought the cycle for Rs P, then the cost price of the cycle for A was:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs \(\frac{10}{9}\)P
In a chain of sales each percentage is taken on the price the seller paid, so the factors multiply: a 20% profit multiplies the price by 1.2 and a 25% loss multiplies it by 0.75.
Let A's cost price be Rs \(x\)
Price B paid \(=1.2x\)
Price C paid \(=0.75\times1.2x=0.9x\)
\(0.9x=P\), so \(\displaystyle x=\frac{P}{0.9}=\frac{10}{9}P\)
A's cost price was Rs \(\frac{10}{9}\)P.