Explanation:

Let's break down the problem:

- Marked Price: The marked price is 25% more than the cost price (C.P).

- Discount: Raman gives a 12% discount on the marked price.

- Profit: After the discount, Raman gains Rs. 55.

Now, let's calculate:

1. Let the cost price be Rs. x.

2. The marked price becomes \( x + 0.25x = 1.25x \).

3. After a 12% discount, the selling price is \( 1.25x \times 0.88 = 1.1x \).

4. Since the gain is Rs. 55, the selling price is also \( x + 55 \).

Equating the selling prices:

$$ 1.1x = x + 55 $$

$$ 0.1x = 55 $$

$$ x = 550 $$

- Option 3: Rs 550 ? Correct

The cost price of the radio is Rs. 550.