The ages of two persons are in the ratio of $$5:7$$. Eighteen years ago their ages were in the ratio $$8:13$$. Find their present ages.
The ages of $$'2'$$ persons are in the ratio $$5:7$$
1st person age = $$5x$$
2nd person age = $$7x$$
$$'18'$$ years ago their ratio $$8:13$$
$$\dfrac{5x-18}{7x-18}=\dfrac{8}{13}$$
$$13(5x-18)=8(7x-18)$$
$$65x-234=56 x-144$$
$$65x-56x=234-144$$
$$9x=90$$
$$x=10$$
1st person age = $$5\times 10=50\,yrs$$
2nd person age = $$7\times 10=70\,yrs$$