Ajay is twice as old as Sujay was when Ajay was as old as Sujay is now. The…

Concept: In an age problem, the difference between two people's ages stays constant over time. To find what someone's age was at a past moment, subtract the number of years that have elapsed from their current age. Translate each verbal relationship ("twice as old as", "combined age") into a linear equation in the two current ages, then solve the resulting system.

Applying this to the problem:

1. Let Ajay's current age be A and Sujay's current age be S. The combined age gives A + S = 42.

2. The age gap between them, A − S, stays the same at every point in time.

3. "When Ajay was as old as Sujay is now" refers to (A − S) years ago. At that time Sujay's age was S − (A − S) = 2S − A.

4. Ajay is twice as old (now) as Sujay was then: A = 2(2S − A), which simplifies to 3A = 4S.

5. Substitute A = 4S/3 into A + S = 42: 4S/3 + S = 42, so 7S/3 = 42, giving S = 18.

6. Then A = 42 − S = 42 − 18 = 24.

Cross-check: the age gap is 24 − 18 = 6 years. Six years ago Ajay was 24 − 6 = 18, matching Sujay's current age as required. At that same moment Sujay was 18 − 6 = 12, and 24 is indeed twice 12, confirming the relationship.

So Ajay's current age is 24 years.