Ten years ago, Kumar was three times as old as Sailesh. Ten years hence, Kumar will be only twice as old as Sailesh. Find the present age of Kumar in years.

Introduction / Context:
This is another linear age problem involving two time references, 10 years ago and 10 years hence. Kumar and Sailesh have a three times relation in the past and a two times relation in the future. From these relationships, we must determine Kumar's present age. Problems like this are standard in the topic problems on ages in aptitude tests.

Given Data / Assumptions:
Ten years ago, Kumar was three times as old as Sailesh. Ten years from now, Kumar will be twice as old as Sailesh. We need to find the present age of Kumar in years. Ages are assumed to be positive integers.

Concept / Approach:
We assign variables to the present ages, then use the past and future conditions to form two linear equations. When an age is described "ten years ago", we subtract 10 from the present age; "ten years hence" means we add 10. Solving the system of equations gives both present ages, and we can then select Kumar's age.

Step-by-Step Solution:
Step 1: Let Kumar's present age be K years and Sailesh's present age be S years.Step 2: Ten years ago, Kumar's age was K - 10 and Sailesh's age was S - 10. The condition says K - 10 = 3 * (S - 10).Step 3: Ten years from now, their ages will be K + 10 and S + 10. The condition says K + 10 = 2 * (S + 10).Step 4: From K - 10 = 3S - 30, we get K = 3S - 20.Step 5: Substitute K = 3S - 20 into K + 10 = 2S + 20 to obtain (3S - 20) + 10 = 2S + 20.Step 6: Simplify: 3S - 10 = 2S + 20, so S = 30 years.Step 7: Substitute back to find K: K = 3 * 30 - 20 = 70 years. Thus, Kumar is 70 years old at present.

Verification / Alternative check:
Ten years ago, Kumar was 60 years old and Sailesh was 20 years old. At that time, 60 is three times 20, which satisfies the first condition. Ten years from now, Kumar will be 80 years old and Sailesh will be 40 years old, and 80 is twice 40, which satisfies the second condition. Therefore, the solution is correct and consistent with all the given information.

Why Other Options Are Wrong:
If Kumar were 50, 60, or 40 years old at present, substituting those values into the equations would fail to satisfy both the past three times relation and the future twice relation. Only a present age of 70 years for Kumar produces valid ages for both people at both time points, so the other options must be rejected.

Common Pitfalls:
As with similar problems, learners may confuse which person is older, misapply the time shifts, or mis-handle the algebra. It is important to clearly label present ages, carefully adjust for ten years ago and ten years hence, and then solve the equations in an orderly fashion.

Final Answer:
Kumar's present age is 70 years.