Question: The ages of two girls are in the ratio of 5:7. Eight years ago their ages were in the ratio 7:13. Find their present ages.

Solution:

Let the ratio of the ages of two girls be 5x:7x.

Given,

Eight years ago their ages were in the ratio 7:13.
or, \dfrac{5x -8}{7x -8} = \dfrac{7}{13}

or, 13(5x -8) = 7(7x -8)

or, 65x - 104 = 49x -56

or, 65x -49x = 104 -56

or, 16x = 48

or, x = \dfrac{48}{16}

\therefore x = 3

Present age of one girl is 5x = 5×3 = 15 years.
Present age of the other girl is 7x = 7×3 = 21 years.

Therefore, the required present ages of the two girls are 15 years and 21 years respectively.