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

Introduction / Context:
This problem on ages involves two people, Ravali and Swarna, with a known difference between their present ages and a future condition relating their ages. Such questions test the ability to convert verbal age relationships into algebraic equations and solve them accurately. They are commonly found in aptitude and competitive exams under the topic problems on ages.

Given Data / Assumptions:
The difference between the present ages of Ravali and Swarna is 9 years. After 7 years, the age of Ravali will be twice the age of Swarna. We assume ages are measured in whole years. We are required to find Ravali's age after 4 years from now.

Concept / Approach:
We express both unknown ages using variables and then use the given difference and the future age condition to form equations. The idea is to represent future ages using present ages plus the number of years and then apply the specified relationship, here "twice". Solving the resulting equations gives the present ages, from which we can find the required future age of Ravali.

Step-by-Step Solution:
Step 1: Let the present age of Ravali be R years and the present age of Swarna be S years.Step 2: The difference condition gives R - S = 9.Step 3: After 7 years, Ravali will be R + 7 years old and Swarna will be S + 7 years old.Step 4: At that time, Ravali's age will be twice Swarna's age, so R + 7 = 2 * (S + 7).Step 5: Expand the equation: R + 7 = 2S + 14, so R = 2S + 7.Step 6: Substitute R = 2S + 7 into R - S = 9 to get (2S + 7) - S = 9.Step 7: Simplify: S + 7 = 9, so S = 2. Then R = S + 9 = 11.Step 8: Ravali's age after 4 years will be R + 4 = 11 + 4 = 15 years.

Verification / Alternative check:
At present, Ravali is 11 years old and Swarna is 2 years old. The difference is 9 years, which matches the given data. After 7 years, Ravali will be 18 years old and Swarna will be 9 years old. At that time, Ravali's age is exactly twice Swarna's age, since 18 = 2 * 9. Therefore, our solution is consistent, and Ravali will indeed be 15 years old after 4 years.

Why Other Options Are Wrong:
If Ravali were 16 years old after 4 years, her present age would be 12 years, leading to inconsistent values for Swarna and violating the future twice-age condition. If Ravali were 20 or 21 years old after 4 years, her present age would be 16 or 17 years, respectively, which again cannot satisfy both the age difference of 9 years and the twice relation after 7 years. Hence, these options do not fit the given conditions.

Common Pitfalls:
Students sometimes reverse the age difference and write S - R = 9 instead of R - S = 9, which leads to negative values or wrong answers. Another common error is to forget that both ages increase by the same amount (7 years) when moving into the future. Careful equation setup based on the statements is essential in problems on ages.

Final Answer:
Ravali will be 15 years old after 4 years.