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 it for A was = ?

Answer: Option D

Let the CP_A = 100x
∴ CP_B = 100x + 20% of 100x = 100x + 20x = 120x
And CP_C = 120x - 25% of 120x = 120x - 30x = 90x
According to question,
90x = P
⇒ x = $$\frac{P}{90}$$
∴ CP_A = $$100\times \frac{P}{90}=\frac{10P}{9}$$