The present age of A is twice the present age of B. After 8 years, the age of B will be four times the present age of C. If C celebrated his fifth birthday 9 years ago, what is the present age, in years, of A?

Introduction / Context:
This age problem connects three people, A, B and C, through simple relationships involving multiples and a time shift. The age of C is given indirectly through a birthday reference in the past. Such questions are common in aptitude tests to assess whether you can decode age information spread across different time points and assemble it into a coherent set of equations.

Given Data / Assumptions:

• The present age of A is twice the present age of B.
• After 8 years, the age of B will be four times the present age of C.
• C celebrated a fifth birthday 9 years ago.
• We must find the present age of A.
• Ages are given in years and are positive.

Concept / Approach:
We start by determining the present age of C from the statement about the fifth birthday. Then we use the future relation of B age after 8 years in terms of C present age to find B present age. Finally, we use the relation that A is twice B to find A present age. This approach shows how to step through a chain of age relationships in a logical order.

Step-by-Step Solution:
Step 1: C celebrated a fifth birthday 9 years ago. Step 2: That means 9 years ago C age was 5 years. Step 3: Therefore, C present age is 5 + 9 = 14 years. Step 4: After 8 years, B age will be four times C present age. Step 5: C present age is 14 years, so after 8 years B age will be 4 * 14 = 56 years. Step 6: If B age after 8 years is 56 years, then B present age is 56 - 8 = 48 years. Step 7: A present age is twice the present age of B. Step 8: Therefore A present age is 2 * 48 = 96 years. Step 9: Hence, A is 96 years old now.

Verification / Alternative check:
Verify each relation with the obtained ages. C is 14 years old now, so 9 years ago C was 14 - 9 = 5 years old, matching the birthday information. B is 48 years old now, so after 8 years B will be 48 + 8 = 56 years old. Four times C present age is 4 * 14 = 56 years, which matches B future age. A present age is 96 years, which is exactly twice 48, confirming the relation between A and B. All conditions in the problem are satisfied.

Why Other Options Are Wrong:
Option A (88 years) would mean B present age is 44, and then B age after 8 years would not equal four times C age, so the condition fails.
Option C (92 years) similarly gives inconsistent values for B and C when checked against the given relationships.
Option D (84 years) fails to make A exactly twice the correct B age that fits the relation with C.

Common Pitfalls:
Learners sometimes misread the statement about the fifth birthday and treat 5 years as the current age rather than the age 9 years ago. Another error is to apply the multiple 4 to B present age instead of B future age as specified. Carefully reading each time reference and applying the correct order of operations is crucial for solving such age chain problems accurately.

Final Answer:
The present age of A is 96 years.