- Alice is as old as Bob will be when Alice is twice the age that Bob was when Alice’s age was half the sum of their present ages.
- The sum of the digits of Alice’s current age and the sum of the digits of Bob’s current age are equal.

If I told you if the difference between the digits in one of their ages is 3 or not - you will be able to tell me their ages.

What are the current ages of Alice and Bob, given that each of their ages is less than 100?

(In reply to

solution?? by Charlie)

I've got the same conclusion 3A=4B

from 2*(.5*(A+B)-d)-d=A and the solution is imminent, simplifying after replacing d=A-B.

Clearly (36,27) & (72,54) qualify as valid answers for the equation but not for the story.

One cannot tell what was BOB's age when ALICE was 31.5- i.e, half of 63: clearly we want integer ages, - unless they have the birthdays on the same day.

1.Assuming that is intentional on the part of the author- a "NO" answer steers as towards (72,54) while "YES" leaves us with bad taste about the coherence of the text.

2. If it was overlooked by the creator of the puzzle - a small correction, stating that the guys share the same birthday date (not the date of birth), puts the problem to bed.