Question

Two years hence a boy will be two times as old as a girl. Before four years, he was three times as old as the girl was. Find their present age.​

Answer 1

Step-by-step explanation:

Let the present age of the boy be x

And present age of the girl be y

Case 1:-

Two years hence (later):-

Age of boy = x + 2

Age of girl = y + 2

Given, the boy will be two times as old as the girl.

⇢ x + 2 = 2(y + 2)

⇢ x + 2 = 2y + 4

⇢ x - 2y = 4 - 2

⇢x - 2y = 2.....(i)

Case 2:-

Four years ago:-

Age of boy = x - 4

Age of girl = y - 4

Given, the boy was three times as old as the girl.

⇢x - 4 = 3(y - 4)

⇢x - 4 = 3y - 12

⇢x - 3y = -12 + 4

⇢ x - 3y = -8......(ii)

Subtracting equation (ii) from (i)

⇢x - 2y - (x - 3y) = 2-(-8)

⇢x - 2y -x + 3y = 2 + 8

⇢ y = 10

Substituting y = 10 in equation (i)

⇢x - 2y = 2

⇢x - 2(10) = 2

⇢ x = 2+20 = 22

We have:-

• x = 22

• y = 10

Therefore:-

⇝Present age of the boy = 22 years

⇝Present age of the girl = 10 years