At what temperature, Celsius and Fahrenheit readings will be same?

The conversion formula between Celsius ($C$) and Fahrenheit ($F$) scales is given by:
$$F=\frac{9}{5}C+32$$

To find the temperature where both readings are identical, set $F=C=x$:

$$x=\frac{9}{5}x+32$$

$$x-\frac{9}{5}x=32$$

$$-\frac{4}{5}x=32$$

$$x=\frac{32\times -5}{4}$$

$$x=-40$$

Therefore, the scales show the exact same reading at $-40^{\circ }$.