Question

The ages of two persons are in the ratio 5 : 7. Eighteen years ago their ages were in the ratio 8 : 13. Find their present ages.

Answer 1

Let the present ages of the two persons be '5x' and '7x' years.
Ratio of their present ages = 5 : 7.
Eighteen years ago, their ages were (5x $-$ 18) and (7x $-$ 18), respectively.
But eighteen years ago the ratio of their ages was 8 : 13.
So, $\frac{5x-18}{7x-18}$ = $\frac{8}{13}$
13(5x $-$ 18) = 8(7x $-$ 18)
65x $-$ 234 = 56x $-$ 144
65x $-$ 56x = 234 $-$ 144
9x = 90
x = $\frac{90}{9}$ = 10
So, their ages are 5x = 5$\times$10 = 50 years and 7x = 7 $\times$ 10 = 70 years.