Question

The ratio of the father and son is 19:9, Eight years ago the ratio of their ages were 3:1, Father's present age is

Answer 1

The ratio of the age of father and son is 19 : 9 (given)

Eight years ago,

The ratio of the age of father and son is 3 : 1 (given)

We have to find the present age of father and son.

So,

Let the present age of father be 19x

And present age of son be 9x

Thus, eight years ago :

Age of father = 19x - 8

Age of son = 9x - 8

According to Question,

$\leadsto\sf\dfrac{19x-8}{9x-8}=\dfrac{3}{1}\\\leadsto\sf{1(19x-8)=3(9x-8)}\\\leadsto\sf{19x-8=27x-24}\\\leadsto\sf{19x-27x=-24+8}\\\leadsto\sf{\cancel-8x=\cancel-16}\\\leadsto\sf{x=}\cancel\dfrac{16}{8}\:^2\\\leadsto\sf{x=2}$

Therefore,

Present age of father = 19x = 19×2 = 38

Present age of son = 9x = 9×2 = 18

Answer 2

Answer: Let present age of father be 8x and that of son be 3x at the ratio 8:3. After 10 years age of father =8x+10 and age of son =3x +10 As per the question (8x +10)/(3x +10) = 2/1 or, 6x +20 = 8x+10 or, 2x = 10 or, x= 5. So the present age of father is 40 years