Question

Two years ago, Sunil was four times as old as his son and two years
hence, twice his age will be equal to six times that of his son. Then the
present age of Sunil is_.
​

Answer 1

Answer :

The present age of Sunil is 34 years

and that of his son is 10 years

Given :

• 2 years ago , Sunil was 4 times as old as his son
• 2 years later ,twice the Sunil's age will be equal to 6 times that of his son.

To Find :

• The present age of Sunil.

Solution :

Let us consider the age of Sunil be x years and that of his son is y years

According to Question :

$\sf \implies x - 2 = 4(y - 2) \\ \\ \sf \implies x - 2 = 4y - 8 \\ \\ \implies \sf x = 4y - 8 + 2 \\ \\ \implies \sf x = 4y - 6 \: ............(1)$

And

$\sf \implies 2(x + 2) = 6(y + 2) \\ \\ \sf \implies x + 2 = 3(y + 2) \\ \\ \implies \sf x + 2 = 3y + 6 \\ \\ \implies \sf x = 3y + 6 - 2 \\ \\ \sf \implies x = 3y + 4 \: ...........(2)$

Comparing equation (1) and (2) we have :

$\sf \implies4y - 6 = 3y + 4 \\ \\ \sf \implies4y - 3y = 4 + 6 \\ \\ \bf \implies y = 10$

Putting the value of y in (2) we get :

$\sf \implies x = 3(10) + 4 \\ \\ \implies \sf x = 30 + 4 \\ \\ \bf \implies x = 34$

Therefore, the present age of Sunil is 34 years and his son is 10 years

Answer 2

~Let,

Age of son be = y

Age of Sunil be = x

~Now,

Two years ago,

Age of son = (y - 2)

Age of Sunil = (x - 2)

According to question,

Age of sunil two years ago was four times age of his son.

Age of sunil = 4(y - 2)

(x - 2) = 4(y - 2)

x - 2 = 4y - 8

x - 4y = -8 + 2

x - 4y = -6 ..............(1)

~And,

Two years hence,

Age of son = (y + 2)

Age of sunil = (x + 2)

According to question,

Twice the age of sunil two years hence will be equal to six times his son's age.

2(x + 2) = 6(y + 2)

2x + 4 = 6y + 12

2x - 6y = 12 - 4

2x - 6y = 8 ............(2)

~Solving (1) and (2) by substitution method,

From (1)

x = -6 + 4y .........(3)

Substitute value of (3) in (2)

2(-6 + 4y) - 6y = 8

-12 + 8y - 6y = 8

2y = 8 + 12

2y = 20

y = 20/2

y = 10

Substituting value of y in (3)

x = -6 + 4y

x = -6 + 4(10)

x = -6 + 40

x = 34

~Age of sunil = x = 34 years