The ratio of two numbers is $$31 : 23$$ and their sum is $$216$$. Find these numbers.
Let the two numbers be $$31x$$ and $$23x$$
Sum of the two numbers = $$216$$
$$\therefore 31x+23x=216$$
$$\Rightarrow 54x=216$$
$$\Rightarrow x=\frac{216}{54}=4$$
$$\therefore$$ One number = $$31x$$ = $$31*4$$ = $$124$$
Other number = $$23x$$ = $$23*4$$ = $$92$$
Thus, the two numbers are $$92$$ and $$124$$.