Question

The sum of two numbers is $184$. If one-third of the one exceeds one-seventh of the other by $8$, find the smaller number.

Answer 1

Let the numbers be $x$ and $(184-x)$
$\Rightarrow \frac{1}{3}x-\frac{184-x}{7}=8$

By solving, we get
$\Rightarrow x=72$
One number is $72$
Other number $=184-72=112$

Thus, the numbers are $72$ and $112$
Hence, the smaller number is $72$