**Question:**

**Calculate the temperature which has same numerical value on Celsius and Fahrenheit scale.**

**Solution:**

Consider two fixed points for the construction of the scale of temperature.

The first fixed point is for the freezing point which is known as lower fixed point.

The second fixed point is for the boiling point which is known as upper fixed point.

Following is the identity that is used for the conversion:

$\frac{\text { reading on any scale }-(L F P)}{(U F P)-(L F P)}=$ constant for all scales

$\frac{C-0}{100}=\frac{F-32}{212-32}$

Let T be the value of temperature that has a same value for Celsius and Fahrenheit scale:

F = C = T

Using the above relation, we can calculate T = -40oF