The sum of the ages of Frank and John is 54 years. 2 years ago, Frank was 4 times as old as John. Find John's age.

Right now, F+J = 54 years

But two years ago, both of them were two years younger than now, so the sum of their age would be different by four years, so:

F+J= 54-4=50 years - eqn 1

Also, Frank was four times as old as John so:

F= 4J - eqn 2

Sub eqn 2 to eqn 1

4J+J=50

5J=50

J=10 years

Since John was age of 10 two years earlier, so his present age would be 10+2= 12 years.

So, now the earlier eqn would look like that

F+12=54

F+12-12=54-12

F=42. Thus, frank is 42 years of age while John is 12 years of age.