An article was sold at 25% gain. Had it been sold for Rs 375 more, then the gain would have been 50%. What is the cost price (in Rs) of the article?

Options

A. 1000
B. 1500
C. 1800
D. 2000

Answer

To find the cost price of the article, let's denote the cost price as \( CP \).

1. **Let the cost price (CP) of the article be \( x \).**
- This is our starting point, where we assume the cost price is \( x \).

2. **Calculate the selling price when sold at a 25% gain.**
- Selling Price (SP) at 25% gain = \( CP + 25\% \text{ of } CP \)
- \( SP = x + 0.25x = 1.25x \)

3. **Calculate the selling price when sold at a 50% gain.**
- Selling Price (SP) at 50% gain = \( CP + 50\% \text{ of } CP \)
- \( SP = x + 0.50x = 1.50x \)

4. **Set up the equation based on the information given.**
- According to the problem, if the article is sold for Rs 375 more than the selling price at 25% gain, it would yield a 50% gain.
- Therefore, we can write the equation:
\[ 1.25x + 375 = 1.50x \]

5. **Solve the equation for \( x \).**
- Rearranging the equation gives:
\[ 375 = 1.50x - 1.25x \]
\[ 375 = 0.25x \]
- Now, divide both sides by 0.25:
\[ x = \frac{375}{0.25} = 1500 \]

6. **Conclusion:**
- The cost price of the article is \( \text{Rs } 1500 \).