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Numerically two thermometers, one in Fahrenheit scale and another in C

June 1, 2025 by rawan239

Numerically two thermometers, one in Fahrenheit scale and another in Celsius scale shall read same at

– 40°

0°

– 273°

100°

This question was previously asked in

UPSC NDA-1 – 2021

Download PDF Attempt Online

The temperature at which both the Fahrenheit and Celsius scales read the same numerical value is -40°.

To find the point where the two scales read the same, we set the temperature in Fahrenheit ($T_F$) equal to the temperature in Celsius ($T_C$) and use the conversion formula: $T_F = T_C$. Let this common temperature be $x$. The conversion formula from Celsius to Fahrenheit is $T_F = T_C \times \frac{9}{5} + 32$. Substituting $x$ for both $T_F$ and $T_C$: $x = x \times \frac{9}{5} + 32$. Solving for $x$: $x – \frac{9x}{5} = 32 \implies \frac{5x – 9x}{5} = 32 \implies \frac{-4x}{5} = 32 \implies -4x = 160 \implies x = \frac{160}{-4} = -40$. Thus, -40°C is equal to -40°F.

Water freezes at 0°C (32°F) and boils at 100°C (212°F). These fixed points are different on the two scales, but there is one point where they intersect.

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