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

Explanation

To solve the problem, we need to relate the temperature in Kelvin (K) to the temperature in Fahrenheit (°F) using the appropriate conversion formulas.

### Step-by-Step Solution:

1. **Understand the Conversion Formula**:
The relationship between Fahrenheit (°F) and Kelvin (K) can be expressed using the formula:
\[ F = \frac{9}{5}(K - 273) + 32 \]
where \(F\) is the temperature in Fahrenheit and \(K\) is the temperature in Kelvin.

2. **Set Up the Equation**:
Given that the temperature in Kelvin is \(x\) K and in Fahrenheit is \(x\) °F, we can substitute \(F\) and \(K\) in the conversion formula:
\[ x = \frac{9}{5}(x - 273) + 32 \]

3. **Simplify the Equation**:
Start by multiplying 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**:
Move all terms involving \(x\) to one side:
\[ 5x - 9x = -2297 \]
This simplifies to:
\[ -4x = -2297 \]

5. **Solve for \(x\)**:
Dividing both sides by -4 gives:
\[ x = \frac{2297}{4} = 574.25 \]

Thus, the value of \(x\) is \(574.25\).

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

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