Question

At what temperature will both Celsius and Fahrenheit’s scales read the same value?
(A) $\text{100 }\!\!{}^\circ\!\!\text{ }$
(B) $\text{180 }\!\!{}^\circ\!\!\text{ }$
(C) $\text{40 }\!\!{}^\circ\!\!\text{ }$
(D) \[-40{}^\circ \]

Answer 1

Hint: Think about what is the relationship between temperature parameters, Celsius and Fahrenheit. Generally we measure body temperature in Fahrenheit. We know the relation, $\text{ }\!\!{}^\circ\!\!\text{ F = ( }\!\!{}^\circ\!\!\text{ C }\!\!\times\!\!\text{ }\dfrac{\text{9}}{\text{5}}\text{) + 32}$. Just assume Celsius is equal to Fahrenheit and solve the equation to get the answer.

Complete step by step solution:
The formulas for converting between degree Celsius and degree Fahrenheit are:
\[\] $\text{ }\!\!{}^\circ\!\!\text{ F = ( }\!\!{}^\circ\!\!\text{ C }\!\!\times\!\!\text{ }\dfrac{\text{9}}{\text{5}}\text{) + 32}$
${}^\circ \text{C=(}{}^\circ \text{F}-32)\times \dfrac{5}{9}$
Now we should know how to find the temperature when both are equal, we use an old algebra trick and just set $\text{ }\!\!{}^\circ\!\!\text{ F = }\!\!{}^\circ\!\!\text{ C}$, and solve the equations given below:
$\text{ }\!\!{}^\circ\!\!\text{ C = ( }\!\!{}^\circ\!\!\text{ C }\!\!\times\!\!\text{ }\dfrac{\text{9}}{\text{5}}\text{) + 32}$
$\Rightarrow \text{ }\!\!{}^\circ\!\!\text{ C}-\text{( }\!\!{}^\circ\!\!\text{ C}\times \dfrac{9}{5})=32$
$\Rightarrow \dfrac{-4}{5}\times \text{ }\!\!{}^\circ\!\!\text{ C}=32$
\[\Rightarrow \text{ }\!\!{}^\circ\!\!\text{ C}=-32\times \dfrac{5}{4}\]
$\Rightarrow \text{ }\!\!{}^\circ\!\!\text{ C}=-40$
So on the Celsius scale the temperature is -40.
Now we have to find the temperature on the Fahrenheit scale.
$\text{ }\!\!{}^\circ\!\!\text{ F = ( }\!\!{}^\circ\!\!\text{ F }\!\!\times\!\!\text{ }\dfrac{\text{9}}{\text{5}}\text{) + 32}$
$\Rightarrow {}^\circ \text{F}-({}^\circ \text{F}\times \dfrac{9}{5})=32$
$\Rightarrow \dfrac{-4}{5}\times {}^\circ \text{F}=32$
$\Rightarrow {}^\circ \text{F}=-32\times \dfrac{5}{4}$$\Rightarrow {}^\circ \text{F}=-40$
$\Rightarrow {}^\circ \text{F}=-40$
So on the Fahrenheit scale, the temperature is -40.
Therefore, at -40 both Celsius and Fahrenheit scales read the same value.

Hence, the correct answer is Option D.

Note: We should be knowing the main difference between the Celsius and the Fahrenheit scale. The boiling point of water is $100\text{ }\!\!{}^\circ\!\!\text{ C}$ while in Fahrenheit scale it is \[212{}^\circ \text{F}\]. Fahrenheit has 0 degrees at the point where the lowest temperature could be achieved in a salt and water mixture. The actual freezing point of water in the Fahrenheit scale is at $32{}^\circ \text{F}$. Fahrenheit is believed to be a superior and precise measuring scale than Celsius since people tend to care more about air temperature than water temperature. We can get a more precise temperature reading in Fahrenheit because it uses more than twice the Celsius scale.