Question

At what temperature, the Celsius and Fahrenheit scale will read the same?
$\begin{align}
  & (A)-10{}^\circ C \\
 & (B)10{}^\circ C \\
 & (C)40{}^\circ C \\
 & (D)-40{}^\circ C \\
\end{align}$

Answer 1

Hint: By using the relation formula of temperature between Celsius and Fahrenheit we will get the answer. We have to choose a temperature on which relation formula will be satisfied.

Complete step by step answer:
 As given in the option we have to find out the temperature in Celsius at with Celsius and the Fahrenheit scale will show the same reading.
The relation formula of temperature between Celsius and Fahrenheit is given below $\dfrac{\text{C}}{\text{5}}\text{=}\dfrac{\text{C-32}}{\text{9}}$....................................(1)
For the same reading of Celsius and Fahrenheit
$\text{C=F}$
Because the given option in the question is in Celsius so we can not replace “C” into “F”. we have to replace “F” into “C”.
So the whole equation will be in the one variable that would be "C". so one equation with a variable can be solved.
Let put $\text{C=F}$ in equation (1)
After putting in the equation we will get $\dfrac{\text{C}}{\text{5}}\text{=}\dfrac{\text{C-32}}{\text{9}}$...............................(2)
 By the shifting rule, we have to solve this equation. So by solving equation (2) we getting the value of "C" that is
 $\text{C=-40}$
So at this temperature, the Celsius scale and the Fahrenheit scale will show the same reading.
Additional Information:
For cross-check our answer we put $\text{C=-40}$ in the equation and find the value of "F" so we get the equation
 $\dfrac{-40}{\text{5}}\text{=}\dfrac{\text{F-32}}{\text{9}}$
By solving the above equation we can the value of "F"
$\text{F=-40}$
Hence prove that our answer is right.
Note:
The student can solve that type of question by option if the temperature relation formula knows. They just have to put all the values one by one in equation(2) and just check RHS and LHS. If we get the RHS=LHS at any option that option will be our answer.