If the sum of two numbers is 137 and their difference is 43, then the smaller number is

Let the two numbers by $x,y$ such that $x>y$ sum of two numbers $=137$

$x+y=137\to \left(1\right)$

Difference of the two number $=43$

$x-y=43\to \left(2\right)$

By adding $\left(1\right)\&\left(2\right)$

$\begin{array}{l}x+y+x-y=137+43\\ 2x=180\\ x=\frac{180}{2}=90\end{array}$

Put $x=90$ in equation $\left(1\right)$ 

$\begin{array}{l}x+y=137\\ 90+y=137\\ y=137-90=47\end{array}$

$\therefore$ the smallest number $\left(y\right)=47$