Question

A man's age is four times the sum of the ages of his three children. In 8 years he will be twice the sum of their ages. What is the man's age?

Answer 1

Let the present sum of the ages of the 3 children be x

So, man's present age = 4x

After 8 years,

Sum of ages of children = x +8 + 8 + 8 = x + 24    

{ Each child's age increases by 8 years}

Man's age = 2( x+ 24)

Also, using our previous expression that stated the man's age ( 4x)

We see that, after 8 years his age will be 4x + 8

But, as his age is also stated to be 2(x+24) after 8 years,

Therefore, 4x+8 = 2(x+24)

4x + 8 = 2x + 48

So, 4x-2x = 48 - 8

2x = 40

So, x = 40/2 = 20 years.

So, 4x = 20 * 4 = 80 years

Answer : The man is of 80 years of age currently

(As 4x expressed his present age, which was 4 times the sum of the ages of his children (x)  )

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