`6%` more is gained be selling a radio for Rs. 475 than by selling for Rs. 451. The C.P. of the radio is-

Options

A. Rs. 400
B. Rs. 434
C. Rs. `440.50`
D. None of these

Answer

To find the cost price (C.P.) of the radio, we can follow these steps:

### Step 1: Understand the problem
We know that selling the radio for Rs. 475 gives a profit that is 6% more than the profit made when selling it for Rs. 451. We need to find the cost price (C.P.) of the radio.

### Step 2: Define the selling prices
Let:
- Selling Price 1 (SP1) = Rs. 451
- Selling Price 2 (SP2) = Rs. 475

### Step 3: Calculate the difference in selling prices
The difference in selling prices is:
\[ \text{Difference} = SP2 - SP1 = 475 - 451 = 24 \text{ Rs.} \]

### Step 4: Understand the profit relationship
According to the problem, the profit from selling at SP2 is 6% more than the profit from selling at SP1. This means:
\[ \text{Profit at SP2} = \text{Profit at SP1} + 6\% \text{ of C.P.} \]

### Step 5: Let the cost price be C
Let the cost price be \( C \).

The profit from selling at SP1 is:
\[ \text{Profit at SP1} = SP1 - C = 451 - C \]

The profit from selling at SP2 is:
\[ \text{Profit at SP2} = SP2 - C = 475 - C \]

### Step 6: Set up the equation
From the profit relationship, we can set up the equation:
\[ 475 - C = (451 - C) + 0.06C \]

### Step 7: Simplify the equation
Now, simplify the equation:
\[ 475 - C = 451 - C + 0.06C \]
\[ 475 - C = 451 - 0.94C \]
Now, add \( C \) to both sides:
\[ 475 = 451 + 0.06C \]
Subtract 451 from both sides:
\[ 475 - 451 = 0.06C \]
\[ 24 = 0.06C \]

### Step 8: Solve for C
Now, solve for \( C \):
\[ C = \frac{24}{0.06} \]
\[ C = 400 \]

### Conclusion
The cost price (C.P.) of the radio is Rs. 400.

---