Question

A man is twice as old as his son. Twelve years ago, the man

was 3 times as old as his son. How old are the father and son
today?

Answer 1

Explanation:

`\underline{ \underline{ \text{Solution}}} :`

Let the present age of father be ' x ' years and that of the son be ' y ' years. From the first condition ,

• x = 2y ••••••• equation ( i )

From the second condition ,

• x - 12 = 3 ( y - 12 ) ••••• equation ( ii )

Substituting the value of x from equation ( i ) in equation ( ii ) :

`\sf{2y - 12 = 3(y - 12)}`

Solve for y ( age of the son ) :

⟿
`\sf{2y - 12 = 3y - 36}`

⟿
`\sf{2y - 3y = - 36 + 12}`

⟿
`\sf{ - y = - 24}`

⟿
`\sf{y = 24}`

Now , Substituting the value of y in equation ( i ) , we get :

`\sf{x = 2 * 24}`

⟿
`\sf{x = 48}`

So, the present age of the father is 48 years and that of the son is 24 years.

Hope I helped ! ツ

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Answer 2

Son's age = 24 years

Man's age = 48 years

Explanation:

Let's take the age of son as x

Man's age = 2x

Twelve years ago,

Son's age= x-12

Man's age= 2x-12

Man is three times as old as his son so,

`(2x - 12)/(x - 12 ) = (3)/(1)`

Solving for x,

2x-12(1) = x-12(3)

2x-12 = 3x-36

2x-3x = -36+12

-x = - 24

x = 24

So if we substitute the values we get,

Son's age = 24 years

Man's age = 48 years

Hope you understand :)