A sells a tube to B at a profit of 20% and B sells it to C at profit of 25 %. If C pays Rs. 225 for it, what did A pay for it?

Options

A. Rs. 100
B. Rs. 125
C. Rs. 150
D. Rs. 175

Answer

To solve the problem step by step, we will first determine the cost price of the tube for A based on the selling price to C.

### Step 1: Understand the Selling Price Flow
- A sells the tube to B at a profit of 20%.
- B sells the tube to C at a profit of 25%.
- C pays Rs. 225 for the tube.

### Step 2: Calculate the Selling Price from B to C
Let the cost price for B be \( CP_B \).
Since B sells the tube to C at a profit of 25%, we can express the selling price (SP) as:
\[ SP_C = CP_B + 0.25 \times CP_B = 1.25 \times CP_B \]
Given that C pays Rs. 225, we have:
\[ 1.25 \times CP_B = 225 \]

### Step 3: Calculate the Cost Price for B
Now, we can find \( CP_B \):
\[ CP_B = \frac{225}{1.25} \]
Calculating this gives:
\[ CP_B = 225 \div 1.25 = 180 \]

### Step 4: Calculate the Selling Price from A to B
Let the cost price for A be \( CP_A \).
Since A sells the tube to B at a profit of 20%, we can express the selling price as:
\[ SP_B = CP_A + 0.20 \times CP_A = 1.20 \times CP_A \]
Now we know that \( SP_B = CP_B \), therefore:
\[ 1.20 \times CP_A = 180 \]

### Step 5: Calculate the Cost Price for A
Now, we can find \( CP_A \):
\[ CP_A = \frac{180}{1.20} \]
Calculating this gives:
\[ CP_A = 180 \div 1.20 = 150 \]

### Conclusion
Thus, A paid Rs. 150 for the tube.