A faulty thermometer has its fixed points marked as 5° and 95°. The temperature of a body as measured by the faulty thermometer is 59°. Find the correct temperature of the body on Celsius scale.

Let ${\mathrm{\theta }}_0$ be the lower fixed point of the faulty thermometer and n be the number of divisions between its lower and the upper fixed points. If a temperature C on Celsius scale
corresponds to temperature q on the scale of faulty thermometer, then

   $\frac{\mathrm{C}-0}{100}=\frac{\mathrm{\theta }-{\mathrm{\theta }}_0}{\mathrm{n}}$   ……..(i)

Here, ${\mathrm{\theta }}_0=5^{\circ };\mathrm{n}=95-5=90\text{ and }\mathrm{\theta }={59}^{\circ }$

Therefore, the Eq. (i) becomes

$\begin{array}{c}\frac{\mathrm{C}-0}{100}=\frac{59-5}{95-5}\\ \mathrm{C}=\frac{54}{90}\times 100\\ \mathrm{C}={60}^{\circ }\mathrm{C}\end{array}$