Let's solve the problem step-by-step:
1. Determine the selling price with profit:
- The cost price (C.P.) is Rs. 200.
- The profit percentage is [tex]\(50\%\)[/tex].
- To find the profit amount, use the formula:
[tex]\[
\text{Profit} = \text{Cost Price} \times \frac{\text{Profit Percentage}}{100} = 200 \times \frac{50}{100} = 200 \times 0.5 = 100 \text{ Rs.}
\][/tex]
- Add the profit to the cost price to get the selling price (S.P.):
[tex]\[
\text{Selling Price} = \text{Cost Price} + \text{Profit} = 200 + 100 = 300 \text{ Rs.}
\][/tex]
2. Find the marked price (M.P.) before discount:
- The selling price after a [tex]\(25\%\)[/tex] discount on the marked price should be equal to Rs. 300 (calculated above).
- Let the marked price be [tex]\( M \)[/tex].
- The discount percentage is [tex]\(25\%\)[/tex], so the selling price after discount is:
[tex]\[
\text{Selling Price} = \text{Marked Price} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right) = M \times \left(1 - \frac{25}{100}\right) = M \times 0.75
\][/tex]
- We know the selling price is Rs. 300, so:
[tex]\[
300 = M \times 0.75
\][/tex]
3. Solve for the marked price (M.P.):
- Divide both sides by [tex]\(0.75\)[/tex]:
[tex]\[
M = \frac{300}{0.75} = 400 \text{ Rs.}
\][/tex]
Therefore, the marked price should be Rs. 400.
The correct answer is:
a. Rs. 400
