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

Introduction / Context:
This question deals with two people, Karan and Shiva, and gives their age relationship 10 years ago and again 10 years in the future. Problems like this require forming equations from time-shifted age statements and solving for the unknown present ages. They are standard in aptitude exams under problems on ages.

Given Data / Assumptions:
Ten years ago, Karan was three times as old as Shiva. Ten years hence, Karan will be twice as old as Shiva. We are required to find the present age of Shiva in years, assuming whole number ages.

Concept / Approach:
We use variables to represent present ages and then translate the past and future conditions into equations. When we go 10 years back, we subtract 10 from the present age; when we go 10 years forward, we add 10. Each statement involving "three times" or "twice" turns into a simple linear equation. Solving the pair of linear equations gives the present ages.

Step-by-Step Solution:
Step 1: Let the present age of Karan be K years and the present age of Shiva be S years.Step 2: Ten years ago, their ages were K - 10 and S - 10. At that time, Karan was three times as old as Shiva, so K - 10 = 3 * (S - 10).Step 3: Ten years hence, their ages will be K + 10 and S + 10. At that time, Karan will be twice as old as Shiva, so 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.Step 7: Therefore, the present age of Shiva is 30 years.

Verification / Alternative check:
If Shiva is 30 years old now, then from K = 3S - 20 we get Karan's present age as 3 * 30 - 20 = 70 years. Ten years ago, Shiva was 20 years old and Karan was 60 years old, and 60 is exactly three times 20. Ten years from now, Shiva will be 40 years old and Karan will be 80 years old, and 80 is exactly twice 40. Thus, all conditions are satisfied.

Why Other Options Are Wrong:
If Shiva were 40 or 60 years old at present, the equations would not be satisfied when checked against both the past and future conditions. The option 70 years corresponds to Karan's present age, not Shiva's, so it is not the required answer. Only 30 years matches all the given relationships.

Common Pitfalls:
Common mistakes include mixing up who is older, misplacing the time shifts (adding instead of subtracting 10, or vice versa), or forming equations from the wrong time frame. Carefully distinguishing between ages 10 years ago, present ages, and ages 10 years hence is crucial to avoid errors.

Final Answer:
The present age of Shiva is 30 years.