A man sold a car for Rs 42,000 at a loss of 16%. What was the cost price of the car?

Options

A. Rs. 68,000
B. Rs 50,000
C. Rs 26,000
D. Rs 26,250

Answer

To find the cost price (CP) of the car when it was sold for Rs 42,000 at a loss of 16%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Selling Price (SP), Cost Price (CP), and Loss Percentage:**
- The formula for selling price when there is a loss is:
\[ SP = CP - \text{Loss} \]
- The loss can also be expressed as a percentage of the cost price:
\[ \text{Loss} = \frac{\text{Loss Percentage}}{100} \times CP \]

2. **Set up the equation:**
- Given that the selling price (SP) is Rs 42,000 and the loss percentage is 16%, we can express the loss in terms of CP (let's denote CP as \( X \)):
\[ SP = CP - \left(\frac{16}{100} \times CP\right) \]
- This simplifies to:
\[ 42000 = X - \left(\frac{16}{100} \times X\right) \]

3. **Combine the terms:**
- The equation can be rewritten as:
\[ 42000 = X - 0.16X \]
- This simplifies to:
\[ 42000 = 0.84X \]

4. **Solve for CP (X):**
- To find \( X \), divide both sides by 0.84:
\[ X = \frac{42000}{0.84} \]

5. **Calculate the value:**
- Performing the division:
\[ X = 50000 \]

6. **Conclusion:**
- The cost price of the car is Rs 50,000.

### Final Answer:
The cost price of the car is Rs 50,000.

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