A thermometer reads 0$^{o}$C as 10 $^{o}$C and 100$^{o}$C as 90$^{o}$C then ;

Find the correct temperature if the thermometer reads 20$^{o}$C

Temperature on any scale can be easily converted into different scale by the following formula

$\dfrac{T - T_f}{T_b - T_f} = \text constant$

where

$T$ = Reading of thermometer

$T_f$ = Freezing point of water

$T_b$ = Boiling Point of water

So here we will equate the reading of two scale namely, thermometer and actual scale.

$\dfrac{20 - 10}{90 - 10} = \dfrac{x - 0}{100 - 0}$

$\dfrac{10}{80} = \dfrac{x}{100}$

$x = 12.5 ^oC$