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?

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Answer 1 · 2017-09-25T07:07:58

John's present age is 8 years.

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
$y = 5x$

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

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.