Question

Divide 184 into two parts such that one - third of one part may exceed one - seventh of other part by 8.

Answer 1

Let one part be $x$ then other part will be $184-x$

One - third of $x=\frac{x}{3}$

One-seventh of other part $=\frac{184-x}{7}$

According to the question,

$\frac{x}{3}=\frac{184-x}{7}+8$

$\Rightarrow$ $\frac{x}{3}=\frac{184-x+56}{7}$

$\Rightarrow$ $7x=3(240-x)$

$\Rightarrow$ $7x=720-3x$

$\Rightarrow$ $10x=720$

$\therefore$ $x=72$

$\therefore$ $184-x=184-72=112$

$\therefore$ The required two numbers are $72$ and $112.$