Question

the ages of A and B are in the ratio 5 ratio 3 after 6 years their ages will be in the ratio 7 ratio 5 find present ages​

Answer 1

$given \: \\ ratio \: of \: present \: age = \frac{5}{3} \\ \\ let \: \: their \: \: present \: \: ages \: \: be \: 5x \: and \: 3x \\ \\ 6years \: \: later \: their \: ages \: will \: be \\ \: 5x + 6 \: and \: 3x + 6$

$also \: \\ \frac{5x + 6}{3x + 6} = \frac{7x}{5x} \ \\ \\ \ = > {25x}^{2} + 30 = {21x}^{2} + 42 \\ = > {4x}^{2} = 12x \\ 4x = 12 \\ x = 3$

$present \: ages \: are \\ 5x = 5 \times 3 = 15years \\ \\ and \: \\ 3x = 3 \times 3 = 9years$

Answer 2

Present ages

A = 5x
B = 3x

After 6 yrs

A = 5x + 6
B = 3x + 6

Acc.to que :

5x + 6 / 3x + 6 = 7 / 5
( 5x + 6 ) 5 = ( 3x + 6 ) 7
25x + 30 = 21x + 42
25x - 21x = 42 - 30
4x = 12
x = 3

Present ages

A = 15 years
B = 9 years