The difference between the selling prices of a keyboard at losses of 15% and 25% is Rs 50. Then the cost price of a keyboard is:

Options

A. Rs 240
B. Rs 330
C. Rs 300
D. Rs 500

Answer

To solve the problem step by step, let's denote the cost price of the keyboard as Rs. X.

### Step 1: Understand the Selling Price Formula
The selling price (SP) when there is a loss can be calculated using the formula:
\[ \text{SP} = \text{Cost Price} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \]

### Step 2: Calculate Selling Prices for Losses of 15% and 25%
1. **Selling Price at 15% Loss (SP1)**:
\[ SP1 = X \times \left(1 - \frac{15}{100}\right) = X \times \frac{85}{100} = \frac{85X}{100} \]

2. **Selling Price at 25% Loss (SP2)**:
\[ SP2 = X \times \left(1 - \frac{25}{100}\right) = X \times \frac{75}{100} = \frac{75X}{100} \]

### Step 3: Set Up the Equation for the Difference in Selling Prices
According to the problem, the difference between SP1 and SP2 is Rs. 50:
\[ SP1 - SP2 = 50 \]
Substituting the values we calculated:
\[ \frac{85X}{100} - \frac{75X}{100} = 50 \]

### Step 4: Simplify the Equation
Combine the terms on the left side:
\[ \frac{85X - 75X}{100} = 50 \]
This simplifies to:
\[ \frac{10X}{100} = 50 \]

### Step 5: Solve for X
To eliminate the fraction, multiply both sides by 100:
\[ 10X = 5000 \]
Now, divide both sides by 10:
\[ X = 500 \]

### Conclusion
The cost price of the keyboard is Rs. 500.