Seven years ago, the ratio of the ages of Anirudh and Bhavana was 7 : 9. Chandhu is at present 12 years older than Anirudh and 12 years younger than Bhavana. What is Chandhu's present age?

Introduction / Context:
This is a challenging age puzzle in which the ages of three people are related by a past ratio and current fixed differences. The ratio from 7 years ago and the two 12 year differences involving Chandhu allow us to construct equations for Anirudh and Bhavana's present ages. With those, Chandhu's present age follows directly.

Given Data / Assumptions:

• Seven years ago, the ratio of Anirudh's age to Bhavana's age was 7 : 9.
• At present, Chandhu is 12 years older than Anirudh.
• At present, Chandhu is also 12 years younger than Bhavana.
• We need to find Chandhu's present age.

Concept / Approach:
Let the present ages of Anirudh and Bhavana be A and B years. Seven years ago their ages were A - 7 and B - 7, and the given ratio gives (A - 7) / (B - 7) = 7 / 9. Also, Chandhu's present age C satisfies C = A + 12 and C = B - 12, giving B - A = 24. Solving these two equations in A and B yields the present ages, then Chandhu's age is A + 12.

Step-by-Step Solution:
Let A be Anirudh's present age and B be Bhavana's present age. Seven years ago, Anirudh was A - 7 and Bhavana was B - 7. Given (A - 7) / (B - 7) = 7 / 9, so 9(A - 7) = 7(B - 7). This expands to 9A - 63 = 7B - 49. Rearrange: 9A - 7B = 14. (Equation 1) At present, Chandhu is 12 years older than Anirudh and 12 years younger than Bhavana, so B - A = 24. (Equation 2) From B - A = 24, we have B = A + 24. Substitute into Equation 1: 9A - 7(A + 24) = 14. So 9A - 7A - 168 = 14 which simplifies to 2A - 168 = 14. Thus 2A = 182 and A = 91 years. Then B = A + 24 = 91 + 24 = 115 years. Chandhu's present age C = A + 12 = 91 + 12 = 103 years.

Verification / Alternative check:
Check the ratio 7 years ago. Anirudh was 91 - 7 = 84 and Bhavana was 115 - 7 = 108. The ratio 84 : 108 simplifies by dividing by 12 to 7 : 9, which matches the problem. At present, Chandhu is 103, which is 12 years more than 91 and 12 years less than 115, confirming both difference conditions. The solution is internally consistent, even though the ages are unusually large, which is acceptable mathematically.

Why Other Options Are Wrong:
If Chandhu were 91 or 115 years old, he would coincide with Anirudh or Bhavana and not satisfy both 12 year differences. The option "Cannot be determined" is incorrect because the system of equations has a unique solution. The suggestion 87 years does not satisfy both the older and younger relations. Only 103 years fits all the given conditions exactly.

Common Pitfalls:
Some students reject the numerical result because the ages seem too high and conclude the data is insufficient, which is not correct. Another common error is mishandling the ratio equation or forgetting to subtract 7 from both ages for the past ratio. Carefully formulating the equations and trusting the algebraic outcome is crucial here.

Final Answer:
Therefore, Chandhu's present age is 103 years.