The present age of Rajitha is three years less than twice her age 12 years ago. The ratio of the present age of Raj to the present age of Rajitha is 4:9. What will be the age of Raj after 5 years?

Introduction / Context:
This problem relates the present age of Rajitha to her own age 12 years ago and then links her current age to the present age of Raj through a ratio. We must determine how old Raj will be after 5 years. Such problems combine linear equations with simple ratios and are typical in aptitude questions on ages.

Given Data / Assumptions:
The present age of Rajitha is three years less than twice her age 12 years ago. The ratio of the present age of Raj to the present age of Rajitha is 4:9. We are asked to find the age of Raj after 5 years. Ages are given in years and are assumed to be whole numbers.

Concept / Approach:
We first use the relation between Rajitha's present age and her age 12 years ago to form a linear equation and solve for her current age. Then, using the given ratio between Raj and Rajitha, we find Raj's present age. Finally, we add 5 to obtain his age after 5 years. This stepwise approach is efficient and clear.

Step-by-Step Solution:
Step 1: Let Rajitha's present age be Rj years.Step 2: Her age 12 years ago was Rj - 12. Twice that age is 2 * (Rj - 12).Step 3: The problem states that her present age is three years less than twice her age 12 years ago. So Rj = 2 * (Rj - 12) - 3.Step 4: Expand: Rj = 2Rj - 24 - 3, which simplifies to Rj = 2Rj - 27.Step 5: Rearranging gives 2Rj - Rj = 27, so Rj = 27 years.Step 6: The ratio of the present age of Raj to the present age of Rajitha is 4:9, so Raj's present age R satisfies R / 27 = 4 / 9.Step 7: Cross multiply: 9R = 4 * 27 = 108, so R = 108 / 9 = 12 years.Step 8: Raj's age after 5 years will be R + 5 = 12 + 5 = 17 years.

Verification / Alternative check:
Check Rajitha's age condition: Twelve years ago, her age was 27 - 12 = 15 years. Twice that age is 2 * 15 = 30, and three years less than 30 is 27, which matches her present age. For the ratio, Raj is 12 years old and Rajitha is 27 years old, and 12:27 simplifies to 4:9 when both numbers are divided by 3. Adding 5 years gives Raj's age as 17 years, which is consistent with all the given information.

Why Other Options Are Wrong:
If Raj were 16, 19, or 21 years old after 5 years, his present age would be 11, 14, or 16 years respectively. None of these values would produce a ratio of 4:9 with Rajitha's age of 27 years. Therefore, those options are not consistent with the given ratio and must be rejected.

Common Pitfalls:
Some learners misinterpret the phrase "three years less than twice her age 12 years ago" and mistakenly write 2Rj - 12 - 3 instead of 2 * (Rj - 12) - 3. Another common error is to invert the ratio and compute 9:4 instead of 4:9 when relating Raj's age to Rajitha's age. Careful reading of the statement and writing equations step by step avoids these mistakes.

Final Answer:
Raj will be 17 years old after 5 years.