Question

John's father is 5 times older than John and John is twice as old as his sister Alice. In two years, the sum of their ages will be 58. How old is John now?

Answer 1

John's present age is 8 years.

Explanation:

Let John's age be `x`.

Given that :
1. John's father is 5 times older than John

If `y` is the age of John's father, then
`y = 5x`

1. John is twice as old as his sister Alice.
   So if `z` is age of Alice, then

`x = 2z` i.e. `z = x/2`

1. In two years, the sum of their ages will be 58.

In two years.

John will be `x+ 2`
John's father will be `y + 2 = 5x +2` and
Alice will be `z + 2 = x/2 +2`

Therefore
`(x+2) + (5x +2) + (x/2 +2) = 58`

`x+2 +5x +2 + 0.5x +2 = 58`

`x+5x + 0.5x +2 +2 +2 = 58`

`6.5x +6 = 58`

`6.5x = 58-6`

`x = 52/ 6.5`

`x = 520/ 65`

`x = 8` --------John's present age.

Fathers present age `y`= `5x = 40` years.
Alice present age `z` = `0.5x = 4` years.

Answer : John's present age is 8 years.