Question

'A' is twice as old as 'B'. Three year ago 'A
was three times as old as 'B'. How old is 'A
now?
(A) 6 years
(B) 12 years'
(C) 14 years (D) 16 years​

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Given :-

• 'A' is twice as old as 'B'.
• Three year ago 'A'
• was three times as old as 'B'.

To find :-

• Present age of A

Solution :-

Let the present age of A be x years.

Let the present age of B be y years.

As per the first condition :-

• A' is twice as old as 'B'.

A = 2B

x = 2y ----> 1

As per the second condition :-

• Three year ago 'A'was three times as old as 'B'

Ages three years ago :-

• Age of A = x - 3
• Age of B = y - 3
• A was three times as old as B

x - 3 = 3 ( y - 3)

x - 3 = 3y - 9

Substitute value of x from equation 1,

2y - 3 = 3y - 9

- 3 + 9 = 3y - 2y

6 = y

Age of B = y = 6 years.

Substitute value of y in equation 1,

x = 2y = 2 × 6 = 12

•°• Age of A = x = 12 years.

Age of B = 6 years.

$\bf{\huge{\underline{\boxed{\rm{\red{Verification:}}}}}}$

For first case :-

• A' is twice as old as 'B'.

Age of A = 12 years = x

Age of B = 6 years = y

Age of A is twice the age of B,

x = 2 (y)

12 = 2 (6)

12 = 12

LHS = RHS.

For second case :-

• Three year ago 'A' was three times as old as 'B'.

Ages three years ago :-

• Age of A = x - 3 = 12 - 3 = 9 years
• Age of B = y - 3 = 6 - 3 = 3 years.

Age of A was three times as old as B,

A = 3B

9 = 3 ( 3)

9 = 9

LHS = RHS.

Hence verified.