The sum of the cost prices of two bikes is Rs.50,000. The first bike was sold at a profit of 20% and second bike at a loss of 20%. If the selling prices are the same, what is the cost price (in Rs.) of the second bike?

Options

A. 25000
B. 20000
C. 30000
D. 27500

Answer

To solve the problem step by step:

1. **Define Variables**:
Let the cost price of the first bike be \( x \) and the cost price of the second bike be \( y \). According to the problem, we have:
\[ x + y = 50,000 \]

2. **Selling Price of the First Bike**:
The first bike is sold at a profit of 20%. Therefore, the selling price (SP) of the first bike can be calculated as:
\[ SP_1 = x + 0.2x = 1.2x \]

3. **Selling Price of the Second Bike**:
The second bike is sold at a loss of 20%. Therefore, the selling price of the second bike can be calculated as:
\[ SP_2 = y - 0.2y = 0.8y \]

4. **Setting Selling Prices Equal**:
According to the problem, the selling prices of both bikes are the same:
\[ 1.2x = 0.8y \]

5. **Express \( y \) in terms of \( x \)**:
Rearranging the equation \( 1.2x = 0.8y \) gives:
\[ y = \frac{1.2}{0.8}x = 1.5x \]

6. **Substituting \( y \) in the Total Cost Price Equation**:
Substitute \( y \) in the equation \( x + y = 50,000 \):
\[ x + 1.5x = 50,000 \]
\[ 2.5x = 50,000 \]

7. **Solving for \( x \)**:
Dividing both sides by 2.5 gives:
\[ x = \frac{50,000}{2.5} = 20,000 \]

8. **Finding \( y \)**:
Now substitute \( x \) back to find \( y \):
\[ y = 1.5x = 1.5 \times 20,000 = 30,000 \]

9. **Conclusion**:
The cost price of the second bike is \( \text{Rs. } 30,000 \).