Question

Find the temperature at which we get the same reading on both Celsius and Fahrenheit scales.

• A. ${40}^{\circ }\text{C}$
• B. $-{40}^{\circ }\text{C}$
• C. ${20}^{\circ }\text{C}$
• D. $-{20}^{\circ }\text{C}$

Answer 1

The correct option is B $-{40}^{\circ }\text{C}$

Let $t$ be the required temperature on the Celsius scale. Then by using the relation between Celsius and Fahrenheit scales,
$\frac{t}{100}=\frac{t-32}{180}$
$\Rightarrow 180t-100t=-3200$
$\Rightarrow 80t=-3200$
$\therefore t=-40{}^{\circ }\text{C}$