At what temperature, the Celsius and Fahrenheit scale will read the same?

Calculating the temperature at which the Celsius and Fahrenheit scales produce the same reading is the task at hand in this issue. We are aware that the Celsius and Fahrenheit scales are two separate systems for measuring temperature. As a result, we'll talk about both systems and discover why the Celsius and Fahrenheit scales differ. We'll talk about how two scales relate later. We will thus compute our answer using this relationship.

The following formulae can be used to convert between degrees Celsius and degrees Fahrenheit:

${}^{\circ }\mathrm{F}=\left({}^{\circ }\mathrm{C}\times 9/5\right)+32$
${}^{\circ }\mathrm{C}=\left({}^{\circ }\mathrm{F}-32\right)\times 5/9$
When both are equal, we apply an ancient algebraic technique and simply set the temperature to zero.

${}^{\circ }\mathrm{F}={}^{\circ }\mathrm{C}$ and resolve a single equation.
${}^{\circ }\mathrm{C}=\left({}^{\circ }\mathrm{C}\times 9/5\right)+32$
${}^{\circ }\mathrm{C}-\left({}^{\circ }\mathrm{C}\times 9/5\right)=32$
$-4/5\times {}^{\circ }\mathrm{C}=32$
${}^{\circ }\mathrm{C}=-32\times 5/4$
${}^{\circ }\mathrm{C}=-40$
${}^{\circ }\mathrm{F}=\left({}^{\circ }\mathrm{F}\times 9/5\right)+32$
${}^{\circ }\mathrm{F}-\left({}^{\circ }\mathrm{F}\times 9/5\right)=32$
$-4/5\times {}^{\circ }\mathrm{F}=32$
${}^{\circ }\mathrm{F}=-32\times 5/4$
${}^{\circ }\mathrm{F}=-40$
Thus, the temperature is -40 degrees when both the Celsius and Fahrenheit scales are equal.

Hence, the correct answer is option C.