Question

A father’s age now is three times the age that his son was 4 years ago. In

12 years, the father will be twice as old as his son. Find their ages now.

Answer 1

Let ‘s’ be the son’s age 12 years ago.
Let ‘f’ be the father’s current age.

4 years ago, the son was:

s-4

So, his father is currently:

3(s-4)

=

3s-12

Therefore:

f = 3s-12

In twelve years, the son will be:

s+12

And the father will be:

f+12

This can also be written as:

3s-12+12 as the fathers younger age would be f = 3s+12

=

3s

So, we know that s+12 is half the fathers current age, meaning the father is currently 2(s+12) which is equivalent to 2s+24. Also, we know that the father is currently 3 times the sons age 12 years ago, so 3s (proven by the calculations we made above). Therefore, 2s+24=3s which means 24=s. We can then substitute this, and we will receive 24+12 = 36

Son’s current age: 36

We then substitute the son’s age 12 years ago into 2s+24 to give us the father’s age.

2(24)+24 = 72

Father’s current age: 72