Two temperature scales A and B are related by $\frac{A-42}{100}=\frac{B -72}{220}$.  At which temperature, two scales have the same readings?  [WB JEE 2011]

The relation between the temperature scales A and B is given as 

$\frac{A-42}{100}=\frac{B -72}{220}$, so for the two scales to have the same reading, A = B

$\Rightarrow \frac{A-42}{100}=\frac{A -72}{220}$

$\Rightarrow \frac{A-42}{1}=\frac{A -72}{2}$

$\Rightarrow 2A-84=A-72$

$\Rightarrow 2A-A=84-72$

$\Rightarrow A={12}^{\circ }$