Five years ago Raj was one third as old as Rahim. If Raj is 17 years old now, how old is Rahim at present?

Introduction / Context:
This age problem connects the present age of one person with the past ages of two people. It tests the ability to back-calculate ages using simple ratios and then move forward to find the current age of the second person. Such questions are typical in aptitude exams and can be solved efficiently with basic algebra.

Given Data / Assumptions:

• Raj is 17 years old at present.
• Five years ago, Raj was one third as old as Rahim.
• We need to find the present age of Rahim.
• All ages are measured in years and are positive.

Concept / Approach:
The problem gives a relationship between their ages at a past time. We first compute Raj age 5 years ago and then use the given ratio to find Rahim age 5 years ago. After that, we add 5 years to Rahim past age to get his current age. This method uses the idea that ages increase linearly with time and that age differences remain constant.

Step-by-Step Solution:
Present age of Raj = 17 years.Five years ago, Raj age was 17 - 5 = 12 years.At that time, Raj was one third as old as Rahim, so Rahim age 5 years ago was 3 times 12.Rahim age 5 years ago = 3 * 12 = 36 years.To find Rahim present age, add 5 years: 36 + 5 = 41 years.Therefore Rahim is currently 41 years old.

Verification / Alternative check:
Check the relationship 5 years ago: Raj was 12, Rahim was 36.Compute the ratio: 12 : 36 = 1 : 3, so Raj was indeed one third as old as Rahim.Check the present ages: Raj is 17 and Rahim is 41, so the age difference is 24 years.The age difference 5 years ago would also be 24 years, confirming consistency.

Why Other Options Are Wrong:
40 years: If Rahim were 40 now, then 5 years ago he would have been 35, and the ratio 12 : 35 is not 1 : 3.36 years: This is Rahim age 5 years ago, not his current age.48 years: If Rahim were 48 now, then 5 years ago he would have been 43, which does not satisfy the one third relationship with Raj age 12.

Common Pitfalls:
Some learners directly apply the ratio to current ages instead of correctly going back 5 years first.Another mistake is forgetting to add 5 years back after computing Rahim age 5 years ago.Misinterpreting one third as Raj being three times older than Rahim also leads to wrong equations.

Final Answer:
The present age of Rahim is 41 years.