A sells a bicycle to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays 225/- for it. the cost price of the bicycle for A is:

Options

A. a) 110
B. b) 125
C. c) 120
D. d) 150

Answer

To find the cost price of the bicycle for A, we can follow these steps:

### Step 1: Define the Cost Price for A
Let the cost price of the bicycle for A be \( CP_A \). We can assume \( CP_A = 100 \) (this is a hypothetical value to simplify calculations).

### Step 2: Calculate Selling Price for A
A sells the bicycle to B at a profit of 20%.
- Selling Price for A (SP_A) = \( CP_A + 20\% \text{ of } CP_A \)
- \( SP_A = 100 + 0.20 \times 100 = 100 + 20 = 120 \)

### Step 3: Calculate Selling Price for B
B sells the bicycle to C at a profit of 25%.
- Selling Price for B (SP_B) = \( SP_A + 25\% \text{ of } SP_A \)
- \( SP_B = 120 + 0.25 \times 120 = 120 + 30 = 150 \)

### Step 4: Relate Selling Price for C to Given Value
According to the problem, C pays 225 for the bicycle. We have calculated that B sold it for 150. We need to find the relationship between these two.
- Since the selling price we calculated (150) does not match the given selling price (225), we can set up a proportion:
\[ \frac{225}{150} = \frac{CP_A}{100} \]

### Step 5: Solve for Cost Price of A
Cross-multiply to solve for \( CP_A \):
- \( CP_A = \frac{225}{150} \times 100 \)
- Simplifying \( \frac{225}{150} \) gives \( 1.5 \)
- Therefore, \( CP_A = 1.5 \times 100 = 150 \)

### Conclusion
The cost price of the bicycle for A is **150**.

---