At what price should shopkeeper mark a radio that costs him Rs. 1200 In order that he may offer a discount of `20 %` on the marked price and still make a profit of `25 %` ?

Options

A. Rs. 1675
B. Rs. 1875
C. Rs. 2025
D. Rs. 1900

Answer

To solve the problem, we need to determine the marked price (MP) of the radio so that after giving a discount of 20%, the shopkeeper still makes a profit of 25% on the cost price of Rs. 1200.

### Step-by-Step Solution:

1. **Calculate the Selling Price (SP) for a 25% Profit:**
- The cost price (CP) of the radio is Rs. 1200.
- To find the selling price that includes a 25% profit, we use the formula:
\[ SP = CP + \left(\frac{Profit \%}{100} \times CP\right) \]
- Here, \( Profit \% = 25 \).
- Thus,
\[ SP = 1200 + \left(\frac{25}{100} \times 1200\right) = 1200 + 300 = 1500 \]

2. **Determine the Marked Price (MP) Considering the Discount:**
- The shopkeeper offers a discount of 20% on the marked price.
- The selling price (SP) after the discount can be expressed as:
\[ SP = MP - \left(\frac{Discount \%}{100} \times MP\right) \]
- Here, \( Discount \% = 20 \).
- This can be rewritten as:
\[ SP = MP \times \left(1 - \frac{20}{100}\right) = MP \times 0.8 \]

3. **Set the Two Expressions for SP Equal to Each Other:**
- From step 1, we found \( SP = 1500 \).
- Therefore, we set the two expressions for SP equal:
\[ 1500 = MP \times 0.8 \]

4. **Solve for the Marked Price (MP):**
- Rearranging the equation gives:
\[ MP = \frac{1500}{0.8} = 1875 \]

### Final Answer:
The marked price at which the shopkeeper should mark the radio is **Rs. 1875**.