Four years ago, the ratio of the ages of A and B was 3: 5. Six years hence, the ratio of the ages of A and B will be 2: 3. What is the sum (in years) of the present ages of A and B?

Let the ages of A and B four years ago be 3x and 5x respectively.
Therefore, their present ages are:

Present age of A=3x+4
Present age of B=5x+4
Six years from now, their ages will be:

Age of A=(3x+4)+6=3x+10
Age of B=(5x+4)+6=5x+10
According to the question, this ratio will be 2:3:

5x+10
3x+10
​
=
3
2
​

3(3x+10)=2(5x+10)
9x+30=10x+20
10x−9x=30−20⟹x=10
Now substitute x=10 into their present ages:

Present age of A=3(10)+4=34 years
Present age of B=5(10)+4=54 years
Sum of their present ages:

Sum=34+54=88 years