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

Solution :

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

Check :

Ratio of the present age of father and son is 19 : 9 that is given.

Thus,

$\to\sf\dfrac{Present \ age \ of \ father}{Present \ age \ of \ son}=\dfrac{19}{9}$

$\to\sf\dfrac{\cancel{38}^{19}}{\cancel{18}^9}=\dfrac{19}{9}$

(By the table of 2)

$\to\sf\dfrac{19}{9}=\dfrac{19}{9}$

Thus, both sides are equal.

Hence, ages are correct.

Answer 2

Answer:

Given :-

• The ratio of the father and son is 19 : 9. Eight years ago the ratio of their ages were is 3 : 1.

To Find :-

• What is the present age of father.

Solution :-

Let, the present age of father be 19x

And, the present age of son will be 9x

Eight years ago,

Age of father is 19x - 8

And, the age of son will be 9x - 8

According to the question,

⇒ $\sf \dfrac{19x - 8}{9x - 8} =\: \dfrac{3}{1}$

By doing cross multiplication we get,

⇒ $\sf 3(9x - 8) =\: 19x - 8$

⇒ $\sf 27x - 24 =\: 19x - 8$

⇒ $\sf 27x - 19x = - 8 + 24$

⇒ $\sf 8x =\: 16$

⇒ $\sf x =\: \dfrac{\cancel{16}}{\cancel{8}}$

➠ $\sf\bold{\purple{x =\: 2}}$

Hence, the required ages are,

✧ Present age of father = 19x = 19(2) = 38 years

✧ Present age of son = 9x = 9(2) = 18 years

$\therefore$ The present age of father is 38 years .