Avanthi's present age is one-sixth of her father's present age. Her father's age will be twice Kapil's age after 10 years. Kapil's eighth birthday was celebrated two years ago. What is Avanthi's present age?

Introduction / Context:
This is a multi-step age problem involving three people: Avanthi, her father, and Kapil. We are given a fractional relationship between Avanthi's age and her father's age, as well as information about Kapil's age and a future relationship between Kapil and the father. Our aim is to work through these relationships to find Avanthi's present age.

Given Data / Assumptions:

- Avanthi's present age is one-sixth of her father's present age.
- After 10 years, the father's age will be twice Kapil's age at that time.
- Kapil's eighth birthday was celebrated two years ago, so Kapil is currently 10 years old.
- All ages are measured in complete years.

Concept / Approach:
We start by determining Kapil's present age from the birthday information. Then we use the future statement about the father's age being twice Kapil's age after 10 years to find the father's current age. Finally, we use the fractional relationship between Avanthi and her father to compute Avanthi's present age. This problem combines time shifts with proportional relationships.

Step-by-Step Solution:
Step 1: Kapil's eighth birthday was celebrated two years ago, so his present age is 8 + 2 = 10 years. Step 2: Let the father's present age be F years. Step 3: After 10 years, Kapil's age will be 10 + 10 = 20 years. Step 4: After 10 years, the father's age will be F + 10 years. Step 5: The problem states that, after 10 years, the father's age will be twice Kapil's age. So F + 10 = 2 × 20 = 40. Step 6: Solving gives F = 40 − 10 = 30 years. Step 7: Avanthi's present age is one-sixth of her father's age. So Avanthi's age = (1 / 6) × 30 = 5 years.

Verification / Alternative check:
Check all relationships: If the father is 30 years old now and Kapil is 10, then after 10 years they will be 40 and 20 years old respectively, satisfying the condition that the father is twice Kapil's age. Avanthi's age as one-sixth of 30 is 5 years, consistent with the given fraction. All conditions are satisfied simultaneously.

Why Other Options Are Wrong:
Ages of 4, 6, 7, or 8 years for Avanthi would not equal one-sixth of a father's age that fits the future condition with Kapil. For example, if Avanthi were 6 years old, her father would be 36, and the future ages would not give the specified 2 : 1 ratio with Kapil. Only 5 years matches both the fractional relationship and the future age condition.

Common Pitfalls:
Some students misread the birthday information and think Kapil is 8 instead of 10, or they forget to apply the 10-year shift to both the father and Kapil before using the "twice the age" condition. Others attempt to guess Avanthi's age directly without first finding the father's age. A systematic approach avoids these errors.

Final Answer:
Avanthi's present age is 5 years.