A man purchases two clocks A and B at a total cost of Rs. 650. He sells A with 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?

Options

A. Rs. 225, Rs. 425
B. Rs. 250, Rs. 400
C. Rs. 275, Rs. 375
D. Rs. 300, Rs. 350

Answer

To solve the problem step by step, we will denote the cost prices of clocks A and B as \( CP_A \) and \( CP_B \) respectively.

### Step 1: Set up the equations based on the problem statement
We know that the total cost of both clocks is Rs. 650. Therefore, we can write the first equation as:
\[ CP_A + CP_B = 650 \quad \text{(1)} \]

### Step 2: Express selling prices in terms of cost prices
Clock A is sold at a profit of 20%. Therefore, the selling price \( SP_A \) can be expressed as:
\[ SP_A = CP_A + 0.2 \times CP_A = 1.2 \times CP_A \]

Clock B is sold at a loss of 25%. Therefore, the selling price \( SP_B \) can be expressed as:
\[ SP_B = CP_B - 0.25 \times CP_B = 0.75 \times CP_B \]

### Step 3: Set the selling prices equal to each other
According to the problem, the selling prices of both clocks are the same:
\[ SP_A = SP_B \]
Substituting the expressions we derived:
\[ 1.2 \times CP_A = 0.75 \times CP_B \quad \text{(2)} \]

### Step 4: Solve the equations simultaneously
From equation (2), we can express \( CP_B \) in terms of \( CP_A \):
\[ CP_B = \frac{1.2}{0.75} \times CP_A = \frac{12}{7.5} \times CP_A = \frac{8}{5} \times CP_A \]

Now substitute \( CP_B \) in equation (1):
\[ CP_A + \frac{8}{5} \times CP_A = 650 \]
Combining the terms:
\[ \left(1 + \frac{8}{5}\right) CP_A = 650 \]
\[ \frac{13}{5} CP_A = 650 \]

### Step 5: Solve for \( CP_A \)
To find \( CP_A \):
\[ CP_A = 650 \times \frac{5}{13} = 250 \]

### Step 6: Find \( CP_B \)
Now substitute \( CP_A \) back into the equation for \( CP_B \):
\[ CP_B = 650 - CP_A = 650 - 250 = 400 \]

### Final Answer
The purchasing prices of clocks A and B are:
\[ CP_A = 250 \quad \text{and} \quad CP_B = 400 \]