If 6 years are subtracted from the present age of Arun and the result is divided by 18, we obtain the present age of his grandson Gokul. Gokul is 2 years younger than Madan, whose present age is 5 years. What is the present age of Arun?

Introduction / Context:
This age problem links three generations using a simple linear relation. The present age of Arun is connected to the age of his grandson through subtraction and division, and the grandson's age is related to another child, Madan. Translating the language into algebraic expressions makes the solution straightforward.

Given Data / Assumptions:

• If 6 years are subtracted from Arun's present age and the result is divided by 18, we get Gokul's present age.
• Gokul is 2 years younger than Madan.
• Madan's present age is 5 years.
• We assume all ages are in whole years and consistent.

Concept / Approach:
We first compute Gokul's present age using the information about Madan. Then we use the equation involving Arun's age and Gokul's age to solve for Arun. The problem becomes a simple one variable linear equation once we substitute the known values.

Step-by-Step Solution:
Let Arun's present age be A years. We are told that (A - 6) / 18 equals Gokul's present age. Madan's present age is given as 5 years. Gokul is 2 years younger than Madan, so Gokul's age = 5 - 2 = 3 years. Therefore, (A - 6) / 18 = 3. Multiply both sides by 18 to clear the denominator: A - 6 = 3 * 18. Compute 3 * 18 = 54, so A - 6 = 54. Add 6 to both sides to get A = 54 + 6. Thus, A = 60 years.

Verification / Alternative check:
Check the result: Arun is 60 years old now. Subtracting 6 gives 54. Dividing 54 by 18 gives 3, which matches Gokul's age. Gokul being 3 years old is indeed 2 years younger than Madan, who is 5. All given conditions are satisfied, so the solution is confirmed.

Why Other Options Are Wrong:
If Arun were 72 years old, (72 - 6) / 18 = 66 / 18 which is not equal to 3. If he were 54, (54 - 6) / 18 = 48 / 18 is also not 3. For 47 years, (47 - 6) / 18 is not an integer and does not give 3 either. Only 60 years makes the equation match the known age of Gokul.

Common Pitfalls:
A frequent mistake is to mix the operations, for example dividing by 6 instead of subtracting 6, or dividing by 18 at the wrong time. Another error is miscomputing Gokul's age from Madan's age. Writing down the relationship clearly before substituting values helps avoid confusion and calculation slips.

Final Answer:
Therefore, Arun's present age is 60 years.