The ratio of the present ages of Karthik and Kalyan is 4:5. The difference between the present age of Kalyan and the age that Karthik will have 5 years from now is 3 years. What is the sum of the present ages of Karthik and Kalyan?

Introduction / Context:
This question combines ratios of present ages with a difference involving a future age. The present age ratio of Karthik and Kalyan is given, and a condition relates Kalyan's present age to Karthik's age 5 years hence. We must find the total of their present ages. Such problems are standard in aptitude topics dealing with ages and ratios.

Given Data / Assumptions:
The ratio of the present ages of Karthik and Kalyan is 4:5. The difference between the present age of Kalyan and the age Karthik will have 5 years from now is 3 years. We are asked to find the sum of their present ages. All ages are in years.

Concept / Approach:
When present ages are in a ratio, we can represent them as multiple of a common factor. Here, we let Karthik's age be 4k and Kalyan's age be 5k. Then we translate the difference condition involving Karthik's age 5 years later and set up an equation in k. Solving for k yields actual ages, and we can then compute their sum.

Step-by-Step Solution:
Step 1: Let the present age of Karthik be 4k years and the present age of Kalyan be 5k years.Step 2: Five years from now, Karthik's age will be 4k + 5 years.Step 3: The problem states that the difference between Kalyan's present age and Karthik's age 5 years hence is 3 years.Step 4: Since Kalyan is older, we write 5k - (4k + 5) = 3.Step 5: Simplify the equation: 5k - 4k - 5 = 3, which gives k - 5 = 3, so k = 8.Step 6: Therefore, Karthik's present age is 4k = 4 * 8 = 32 years, and Kalyan's present age is 5k = 5 * 8 = 40 years.Step 7: Their total present age is 32 + 40 = 72 years.

Verification / Alternative check:
Check the given condition. The ratio 32:40 simplifies to 4:5, which matches the present age ratio. Five years hence, Karthik will be 37 years old. The difference between Kalyan's present age (40) and 37 is 3 years, exactly as stated. Therefore, all the information fits perfectly, confirming that the sum of their present ages is 72 years.

Why Other Options Are Wrong:
Totals of 56, 62, or 69 years do not correspond to any combination of ages that both satisfy the 4:5 ratio and the condition involving a 3 year difference with Karthik's future age. Only a total of 72 years yields ages of 32 and 40, which satisfy all the constraints.

Common Pitfalls:
One common mistake is to reverse the difference and write (4k + 5) - 5k = 3, which would incorrectly assume Karthik is older even 5 years hence. Another error is forgetting to add 5 only to Karthik's age while leaving Kalyan's present age unchanged in the equation. Careful interpretation of the phrase "difference between the present age of Kalyan and the age of Karthik 5 years hence" is essential.

Final Answer:
The sum of the present ages of Karthik and Kalyan is 72 years.