Question

Present age of a person is four times his son. Eighteen years hence his age will be twice
old as the son. What are their present ages.(Ans.: 36yrs., 9yrs.)​

Answer 1

Answer:

Age of Person - 36yrs, Age of Son - 9yrs.

Step-by-step explanation:

Let the present age of father be x and present age of his son be y.

According to the first statement,

x = 4y

or x - 4y = 0

The statement says that

18 + x = 2( 18 + y)

[As years passby, both of them will get older]

=> 18 + x = 36 + 2y

or x - 2y = 18

Subtracting equation (ii) from equation (i), we get

x - 4y =0

- x - 2y = 18

=> (x - x) + (-4y - -2y) = (0 - 18)

=> -2y = -18

or 2y = 18

Therefore, age of son = y = 18/2 = 9

Substituting y = 9 in equation(i) x = 4y years,

We get, age of the person = x = 4 × 9 = 36 years

Answer 2

• The present age of son = 9 years.
• The present age of his father = 36 years.

Given :–

• Present age of a person is four times his son.
• After eighteen years, his age will be twice old as the son.

To Find :–

• Their present age.

Solution :–

Let,

The age of son be x.

The age of his father be 4x because according to the question, his father is four times older than his son.

After eighteen years,

The age of son be 2(x + 18) because according to the question, after eighteen years, his father's age will be twice old as son.

The age of his father be 4x + 18.

According to the condition,

$\hookrightarrow 4x + 18 = 2(x + 18)$

$\hookrightarrow 4x + 18 = 2x + 36$

$\hookrightarrow 4x - 2x = 36 - 18$

$\hookrightarrow 2x = 18$

$\hookrightarrow x = \cancel \dfrac{18}{2}$

$\hookrightarrow x = 9$

So,

The age of son = x = 9 years.

The age of his father = 4x = 4 × 9 = 36 years.

Hence,

The present age of son and his father is 9 years and 36 years.