Let's solve this step-by-step by defining variables and forming equations based on the given information.

Let:

• $N$ be Naveen's current age.
• $R$ be Rajeev's current age.
• $S$ be Sanjeev's current age.

Step 1: Analyzing the Statements and Forming Equations

1. First Statement: "20 years hence, Naveen's age will be the same as Rajeev's age now."

   • After 20 years, Naveen's age will be $N + 20$.
   • According to the statement, $N + 20 = R$.

2. Second Statement: "20 years hence, he (Naveen) would be half as old as Sanjeev then."

   • After 20 years, Sanjeev's age will be $S + 20$.
   • According to the statement, $N + 20 = \frac{S + 20}{2}$.

3. Third Statement: "Rajeev was half as old as Sanjeev when Naveen was born."

   • When Naveen was born, Naveen's age was 0, so this was $N$ years ago.
   • $N$ years ago, Rajeev's age was $R - N$.
   • $N$ years ago, Sanjeev's age was $S - N$.
   • According to the statement, $R - N = \frac{S - N}{2}$.

Step 2: Setting Up the Equations

From the above statements, we have the following three equations:

1. $N + 20 = R$
2. $N + 20 = \frac{S + 20}{2}$
3. $R - N = \frac{S - N}{2}$

Step 3: Solving the Equations

Substitute $R$ from Equation (1) into the other equations.

From Equation (1): $R = N + 20$

Substitute $R = N + 20$ into Equation (3):

$(N + 20) - N = \frac{S - N}{2}$

This simplifies to: $20 = \frac{S - N}{2}$

Multiply both sides by 2: $40 = S - N$

So, $S = N + 40$

Substitute $S = N + 40$ into Equation (2):

$N + 20 = \frac{(N + 40) + 20}{2}$

Simplify the right side: $N + 20 = \frac{N + 60}{2}$

Multiply both sides by 2: $2(N + 20) = N + 60$

Expanding and simplifying: $2N + 40 = N + 60$

Subtract $N$ from both sides: $N = 20$

Step 4: Substitute $N = 20$ back to find $R$ and $S$

1. From $R = N + 20$: $R = 20 + 20 = 40$

2. From $S = N + 40$: $S = 20 + 40 = 60$

Conclusion

Rajeev's current age is 40 years.

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Would you like more details on any step or have any further questions?

Additional Questions:

1. If Naveen's age increases by another 10 years, what will Rajeev's age be in comparison?
2. How does Sanjeev's age compare to Rajeev's age in terms of growth over time?
3. If we change the time frame from 20 years to 30 years in the first statement, how does that affect Rajeev's age?
4. How would the solution change if Rajeev was originally said to be twice as old as Sanjeev when Naveen was born?
5. Can you generalize this solution for any other initial ages for Naveen, Rajeev, and Sanjeev?

Tip:

When solving age-related problems, try to define the current age of each person and use algebraic equations to represent the given conditions accurately. This method simplifies complex relationships into manageable equations.