Question

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

Answer 1

8 years

Explanation:

Let age of father be f

age of John be j

age of Alice be a

John's father is 5 times as old as John. We can write:

f = 5j

John is twice as old as Alice. We can write:

j = 2a

or

a = j/2

SUM OF ALL OF THEIR AGES (after 2 years) will be 58. We can write:

f+2 + j+2 + a+2 = 58

This becomes:

f + j + a + 6 = 58

f + j + a = 52

Now, we replace third equation with the first two (in bold) and get:

`f + j + a = 52\\5j + j + (1)/(2)j=52\\6.5j=52\\j=8`

So John is 8 years old