An article is sold at 10% loss. Had it been sold for Rs 30 more, the loss would have been 5% only. What is the cost price of the article ?

Options

A. Rs 500
B. Rs 300
C. Rs 200
D. Rs 600

Answer

To find the cost price of the article, we can follow these steps:

1. **Understand the Loss Percentages**:
- The article is sold at a 10% loss.
- If sold for Rs 30 more, the loss would be reduced to 5%.

2. **Define the Variables**:
- Let the cost price of the article be \( CP \).

3. **Set Up the Equations**:
- Selling Price (SP) at 10% loss:
\[ SP = CP - 10\% \text{ of } CP = CP - \frac{10}{100} \times CP = CP \left(1 - \frac{10}{100}\right) = CP \times 0.9 \]
- Selling Price (SP) at 5% loss (when sold for Rs 30 more):
\[ SP + 30 = CP - 5\% \text{ of } CP = CP - \frac{5}{100} \times CP = CP \left(1 - \frac{5}{100}\right) = CP \times 0.95 \]

4. **Equate the Two Selling Prices**:
- From the above, we can write:
\[ CP \times 0.9 + 30 = CP \times 0.95 \]

5. **Solve for CP**:
- Rearranging gives:
\[ CP \times 0.95 - CP \times 0.9 = 30 \]
\[ CP \times (0.95 - 0.9) = 30 \]
\[ CP \times 0.05 = 30 \]
\[ CP = \frac{30}{0.05} \]
\[ CP = 30 \times 20 = 600 \]

6. **Conclusion**:
- The cost price of the article is Rs 600.