Fahrenheit and Kelvin Scales are in agreement at a reading of

$- 40$

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$0$

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$574$

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$273$

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Solution

The correct option is C
$574$

Step 1 Equating both the conversion Formulas
By Equating both the conversion formulas, we will obtain the relation between Kelvin and Fahrenheit Scale
$T_{C} = T_{K} - 273 T_{C} = (T_{F} - 32) \times (\frac{5}{9}) T_{K} - 273 = (T_{F} - 32) \times (\frac{5}{9})$
Step 2 Solving to find at which reading the Fahrenheit and Kelvin Scales are in agreement
We need to find at which value, Kelvin Scale and Fahrenheit Scale will show the same temperature. (So, we can substitute $T_{K}$ in the place of $T_{F}$ , as $T_{K} = T_{F}$ , as per the situation)
Therefore,
$T_{K} - 273 = (T_{F} - 32) \times (\frac{5}{9}) T_{K} - 273 = (T_{K} - 32) \times (\frac{5}{9}) T_{K} - 273 = (\frac{5}{9}) (T_{K}) - (\frac{5}{9}) (32) T_{K} - 273 = (\frac{5}{9}) (T_{K}) - 17.78 T_{K} - (\frac{5}{9}) (T_{K}) = 273 - 17.78 \frac{9 T_{K} - 5 T_{K}}{9} = 255.22 \frac{4 T_{K}}{9} = 255.22 T_{K} = 255.22 \times \frac{9}{4} T_{K} = 574.245$
By rounding off, we will get $T_{K} = 574$
Therefore, the reading at which the Fahrenheit and Kelvin Scale will be equal is at $574$
Hence option (c) $574$ is correct

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