The difference between the present ages of Avanthi and Kapil is 9 years. After 7 years, Kapil age will be twice the age of Avanthi. What will be Kapil age after 4 years from now?

Introduction / Context:
This problem on ages involves two people and a mix of present and future ages. Such questions test your ability to convert verbal statements into simultaneous equations and then to extract the exact value requested, which here is Kapil age after a certain number of years. The question also trains you to handle the phrase twice the age carefully, which indicates a multiplication relationship rather than a simple difference.

Given Data / Assumptions:

• The difference between the present ages of Avanthi and Kapil is 9 years.
• After 7 years, Kapil age will be twice the age of Avanthi at that time.
• We need to find Kapil age after 4 years from now.
• Ages are measured in whole years and both people age normally over time.

Concept / Approach:
Whenever you see words like twice, three times, or difference of ages, it suggests setting up algebraic equations. Let the present ages be variables, use the difference condition to form one equation, and use the future double age condition to form another equation. Solving these two linear equations in two variables gives the present ages. Then it is easy to move forward in time to find Kapil age after 4 years. The main skill is careful translation of the words into correct algebraic expressions.

Step-by-Step Solution:
Step 1: Let the present age of Avanthi be A years and the present age of Kapil be K years. Step 2: Use the difference condition to write K − A = 9, assuming Kapil is older. Step 3: After 7 years, Avanthi age becomes A + 7 and Kapil age becomes K + 7. Step 4: The statement that after 7 years Kapil age is twice Avanthi age becomes K + 7 = 2 × (A + 7). Step 5: Solve the pair of equations K − A = 9 and K + 7 = 2 × (A + 7). You will obtain A = 2 and K = 11. Step 6: Kapil age after 4 years will be K + 4 = 11 + 4 = 15 years.

Verification / Alternative check:
Check with the found ages. At present Kapil is 11 and Avanthi is 2, so the difference is 9 years as given. After 7 years, Kapil will be 18 and Avanthi will be 9, and 18 is exactly twice 9. After 4 years, Kapil will indeed be 15 years old. All conditions match the problem statement, so the solution is consistent.

Why Other Options Are Wrong:
Option 16: This would imply Kapil present age is 12, which breaks the given relationships. The future double condition would not hold.
Option 18: If Kapil age after 4 years were 18, his present age would be 14, again failing the given conditions when checked.
Option 20: This would mean Kapil is 16 now; substituting into the equations does not satisfy the difference and double constraints.
Option 22: This would make Kapil even older, and checking with the algebra shows the data cannot all be satisfied at once.

Common Pitfalls:
Learners often confuse who is older and write A − K = 9 instead of K − A = 9. Another mistake is to forget that both ages increase by the same amount when you move several years into the future, so some people write incorrect expressions such as K + 7 = 2A. Always express the age at a future time as present age plus the number of years, and only then apply the multiple relationship.

Final Answer:
Kapil age after 4 years will be 15 years.