Question

The temperature at which centigrade and Fahrenheit scale give the same reading (in degree) is,
(A) $- 40$
(B) $40$
(C) $- 30$
(D) $30$

Answer 1

Celsius and Fahrenheit are two temperature scales. The Celsius and Fahrenheit scale have one point at which they intersect. They are equal at$- 40^\circ C$and$- 40^\circ F$. The simple way to find when two temperature scales are equal to each other is to set the conversion factor for the two scales equal to each other and solve for temperature.

Complete step-by-step solution:
To set degrees Celsius and degree Fahrenheit equal to each other using the conversion formula between the two scales:

$$^\circ F = \left( {^\circ C \times \dfrac{9}{5}} \right) + 32 \\\ ^\circ C = \left( {^\circ F - 32} \right) \times \dfrac{5}{9} \\\$$

It does not matter which equating you use; simple use x instead of degrees Celsius and degree Fahrenheit, you can solve this problem by solving for ’x’,

$$^\circ C = \left( {^\circ F - 32} \right) \times \dfrac{5}{9} \\\ x = \dfrac{5}{9} \times \left( {x - 32} \right) \\\ x = \left( {\dfrac{5}{9}} \right)x - 17.778 \\\ 1x - \left( {\dfrac{5}{9}} \right)x = - 17.778 \\\ 0.444x = - 17.778 \\\ x = - 40^\circ C \\\ or \\\ x = - 40^\circ F \\\$$

Working using the other equation, you get the same answer,

$$^\circ F = \left( {^\circ C \times \dfrac{9}{5}} \right) + 32 \\\ x - \left( {x \times \dfrac{9}{5}} \right) = 32 \\\ \dfrac{{ - 4}}{5} \times x = 32 \\\ x = - 32 \times \dfrac{5}{4} \\\ x = - 40^\circ C \\\ or \\\ x = - 40^\circ F \\\$$

In conclusion, the option (A) is the correct answer.

Additional Information: You can set two scales equal to each other to find when any of them intersect, sometimes it is easier to just look up the equivalent temperature.
We can also practice converting between temperature scales:
Fahrenheit to Celsius
Celsius to Fahrenheit
Celsius versus centigrade

Note: The Fahrenheit and Celsius scales have one point at which they intersect, they are equal at$- 40^\circ C$ and $- 40^\circ F$.