Question

10 years ago mother was 4 times as old as her son. After 3 years ratio of their ages will be 15:7. Find their present age.​

Answer 1

Let 'x' be the son's present age and 'y' be the mother's present age

According to first condition;

y - 10 = 4(x - 10)

y - 10 = 4x - 40

4x - y = 40 - 10

4x - y = 30 ... (A)

multiplying throughout by 7, we get

28x - 7y = 210 ... (i)

According to second condition;

$\frac{y + 3}{x + 3} = \frac{15}{7}$

7y + 21 = 15x + 45

15x - 7y = 21 - 45

15x - 7y = -24 ... (ii)

subtracting (ii) from (i)

=> 28x - 7y = 210

( – ) 15x - 7y = -24

......(-).....(+)......(+)

__________________

13x = 234

x = $\frac{234}{13}$

x = 18

substituting in (A)

4(18) - y = 30

y = 72 - 30

y = 42

Hence, the present ages of the son and his mother are 18 and 42 years respectively.