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

Options

A. a)`9/10P`
B. b)`10/9P`
C. c)`1/20P`
D. d)`9/20P`

Answer

To solve the problem step by step, we will first establish the relationships between the cost prices and selling prices of the cycle as it changes hands from A to B and then from B to C.

### Step-by-Step Solution

1. **Assume the Cost Price for A**:
Let's assume the cost price of the cycle for A is Rs 100.

**Hint**: Start with a simple assumption to make calculations easier.

2. **Calculate Selling Price for A to B**:
A sells the cycle to B at a profit of 20%.
- Profit = 20% of 100 = \( \frac{20}{100} \times 100 = 20 \)
- Selling Price for A to B = Cost Price + Profit = \( 100 + 20 = 120 \)

**Hint**: Remember that selling price can be calculated by adding profit to the cost price.

3. **Calculate Cost Price for B**:
The cost price for B is Rs 120 (the price at which A sold the cycle to B).

**Hint**: The selling price for A becomes the cost price for B.

4. **Calculate Selling Price for B to C**:
B sells the cycle to C at a loss of 25%.
- Loss = 25% of 120 = \( \frac{25}{100} \times 120 = 30 \)
- Selling Price for B to C = Cost Price - Loss = \( 120 - 30 = 90 \)

**Hint**: Selling price at a loss is calculated by subtracting the loss from the cost price.

5. **Relate Selling Price for C to Cost Price for A**:
We know that C bought the cycle for Rs P, which is Rs 90.
- We need to find the cost price of the cycle for A when C's cost price is Rs P (90).
- We set up the proportion:
\[ \text{If Cost Price for A} = 100 \text{ then Selling Price for C} = 90 \]
\[ \text{If Cost Price for A} = x \text{ then Selling Price for C} = P \]
- This gives us the equation:
\[ \frac{x}{100} = \frac{P}{90} \]
- Cross-multiplying gives:
\[ x = \frac{P \times 100}{90} = \frac{10P}{9} \]

**Hint**: Use proportions to relate the cost prices and selling prices.

6. **Final Answer**:
Thus, the cost price of the cycle for A is \( \frac{10P}{9} \).

### Summary
The cost price of the cycle for A, when C bought it for Rs P, is \( \frac{10P}{9} \).