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. 301.25
B. 574.25
C. 313
D. 40

Answer

To solve the problem, we need to find the value of \( x \) where the temperature in Kelvin (K) is equal to the temperature in Fahrenheit (°F), given that both are represented by \( x \).

### Step-by-Step Solution:

1. **Understanding the Temperature Conversion Formulas**:
- The relationship between Fahrenheit (°F) and Celsius (°C) is given by:
\[ °F = °C \times \frac{9}{5} + 32 \]
- The relationship between Celsius (°C) and Kelvin (K) is:
\[ K = °C + 273.15 \]

2. **Setting Up the Equations**:
- We are given that the temperature in Kelvin is \( x \) K and in Fahrenheit is \( x \) °F.
- From the Kelvin to Celsius conversion, we can express Celsius in terms of Kelvin:
\[ °C = K - 273.15 = x - 273.15 \]
- Now substituting this into the Fahrenheit equation:
\[ x = (x - 273.15) \times \frac{9}{5} + 32 \]

3. **Simplifying the Equation**:
- Rearranging the equation:
\[ x = \frac{9}{5}(x - 273.15) + 32 \]
- Distributing \( \frac{9}{5} \):
\[ x = \frac{9}{5}x - \frac{9 \times 273.15}{5} + 32 \]
- Converting \( 32 \) to a fraction with a common denominator:
\[ 32 = \frac{160}{5} \]
- Thus, we have:
\[ x = \frac{9}{5}x - \frac{2458.35}{5} + \frac{160}{5} \]
- Combining the constants:
\[ x = \frac{9}{5}x - \frac{2298.35}{5} \]

4. **Isolating \( x \)**:
- Rearranging gives:
\[ x - \frac{9}{5}x = -\frac{2298.35}{5} \]
- Factoring out \( x \):
\[ \left(1 - \frac{9}{5}\right)x = -\frac{2298.35}{5} \]
- Simplifying \( 1 - \frac{9}{5} = -\frac{4}{5} \):
\[ -\frac{4}{5}x = -\frac{2298.35}{5} \]
- Multiplying both sides by \(-\frac{5}{4}\):
\[ x = \frac{2298.35}{4} = 574.5875 \]

5. **Final Value of \( x \)**:
- Rounding to two decimal places, we find:
\[ x \approx 574.25 \]

### Conclusion:
The value of \( x \) is approximately \( 574.25 \).