The temperature of a body on Kelvin scale is found to be x K . When it is measured by Fahrenheit thermometer, it is found to be `x^(@)F` , then the value of x is

Options

A. 40
B. 313
C. `574.25`
D. `301.25`

Answer

To solve the problem, we need to convert the temperature from Kelvin to Fahrenheit and set up an equation based on the given information.

### Step-by-Step Solution:

1. **Understanding the Temperature Scales**:
We know the relationship between Kelvin (K) and Fahrenheit (F) is given by the formula:
\[ F = \frac{9}{5}(K - 273) + 32 \]

2. **Setting Up the Equation**:
According to the problem, the temperature in Kelvin is \( x \) K, and in Fahrenheit, it is \( x^\circ F \). Therefore, we can set up the equation:
\[ x = \frac{9}{5}(x - 273) + 32 \]

3. **Simplifying the Equation**:
First, we will multiply both sides by 5 to eliminate the fraction:
\[ 5x = 9(x - 273) + 160 \]
Expanding the right side:
\[ 5x = 9x - 2457 + 160 \]
Simplifying further:
\[ 5x = 9x - 2297 \]

4. **Rearranging the Equation**:
Now, we will move \( 9x \) to the left side:
\[ 5x - 9x = -2297 \]
This simplifies to:
\[ -4x = -2297 \]

5. **Solving for x**:
Dividing both sides by -4 gives:
\[ x = \frac{2297}{4} \]
Calculating this gives:
\[ x = 574.25 \]

### Final Answer:
The value of \( x \) is \( 574.25 \).