Question

At what temperature, the Celsius and Fahrenheit scales will read the same?
A. \[ - 10^\circ \,{\text{C}}\]
B. \[10^\circ \,{\text{C}}\]
C. \[40^\circ \,{\text{C}}\]
D. \[ - 40^\circ \,{\text{C}}\]

Answer 1

Hint: Use the conversion formula to convert the temperature on Fahrenheit scale to Celsius scale. Substitute \[{T_C}\] for \[{T_F}\] in this formula to get the temperature on Celsius scale.

Formula used:
\[{T_F} = \dfrac{9}{5}{T_C} + 32\]
Here, \[{T_F}\] is the temperature on Fahrenheit scale and \[{T_C}\] is the temperature on Celsius scale.

Complete step by step solution:
We know the conversion formula to convert Fahrenheit temperature to Celsius temperature,
\[{T_F} = \dfrac{9}{5}{T_C} + 32\]
Here, \[{T_F}\] is the temperature on Fahrenheit scale and \[{T_C}\] is the temperature on Celsius scale.
We have given that the certain temperature on Fahrenheit scale and Celsius scale is the same. Therefore, we can substitute \[{T_C}\] for \[{T_F}\] in the above equation.
\[{T_C} = \dfrac{9}{5}{T_C} + 32\]
\[ \Rightarrow {T_C} - \dfrac{9}{5}{T_C} = 32\]
\[ \Rightarrow - \dfrac{4}{5}{T_C} = 32\]
\[ \Rightarrow {T_C} = - \dfrac{{32 \times 5}}{4}\]
\[ \Rightarrow {T_C} = - 40^\circ \,{\text{C}}\]

Therefore, at \[ - 40^\circ \,{\text{C}}\], the Fahrenheit scale and Celsius scale will read the same temperature.

So, the correct answer is “Option D”.

Additional Information:
The lower fix point of Fahrenheit scale is \[32^\circ {\text{F}}\] and the upper fix point is \[212^\circ {\text{F}}\]. The lower fix point of Celsius scale is \[0^\circ \,{\text{C}}\] and upper fix point is \[100^\circ \,{\text{C}}\]. If we have given the temperature on the Fahrenheit scale and we have been asked to determine the corresponding temperature on Celsius scale, we can use the conversion formula,
\[\dfrac{{{T_C} - LFP}}{{UFP - LFP}} = \dfrac{{{T_F} - LFP}}{{UFP - LFP}}\]

Here, LFP is the lower fix point and UFP is the upper fix point. If we put the value of Fahrenheit temperature \[{T_F}\] as \[ - 40^\circ \,{\text{F}}\], after substituting the corresponding LFP and UFP of Fahrenheit scale and Celsius scale, we will get the temperature on Celsius scale as \[ - 40^\circ \,{\text{C}}\].

Note:
We can also solve this question using the formula for converting the temperature on Celsius scale to Fahrenheit scale. The conversion formula is, \[{T_C} = \dfrac{5}{9}\left( {{T_F} - 32} \right)\]. If you substitute \[{T_C}\] for \[{T_F}\] in this equation, the result will be the same.