A Centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $${140^ \circ }.$$  What is the fall in temperature as registered by the Centigrade thermometer?

Solution :
Relation between Celsius scale and Fahrenheit scale is $$\frac{C}{{100}} = \frac{{F - 32}}{{180}}$$
Putting value of $$F = {140^ \circ }$$
$$\eqalign{ & \therefore \frac{C}{{100}} = \frac{{140 - 32}}{{180}} = 0.6 \cr & \therefore C = {60^ \circ } \cr} $$
Hence, fall in temperature = Temperature of boiling water - final temperature
$${100^ \circ }C - {60^ \circ }C = {40^ \circ }C$$