Four friends Raghu, Rajesh, Ramesh, and Ravi completed their graduation in different numbers of years. The one who took the maximum time took eight years to complete graduation, and the one who took the least time took only three years. Ravi took more time only than Raghu and completed his graduation in five years. Ramesh did not take longer time than Rajesh to complete his graduation. Who among the four took the most years to complete graduation?

Introduction / Context:
This is a classic ordering and ranking puzzle involving four friends and the time each took to complete graduation. We know the extreme values (minimum and maximum years) and some relational information about who took more or less time than whom. The goal is to use these clues to determine which friend took the maximum number of years to complete graduation.

Given Data / Assumptions:

• Friends: Raghu, Rajesh, Ramesh, and Ravi.
• All four took different numbers of years to complete graduation.
• The maximum time taken by any one of them is 8 years.
• The minimum time taken is 3 years.
• Ravi took more time only than Raghu and completed graduation in 5 years.
• Ramesh did not take longer time than Rajesh (so Ramesh took less than or equal to Rajesh).

Concept / Approach:
We need to assign unique times to each person from a small discrete set. The specific times we know are 3 years minimum, 8 years maximum, and 5 years for Ravi. With the condition that all times are different, and Ravi took more time only than Raghu, we can place Ravi and Raghu in the order. Then we must use the relation between Ramesh and Rajesh to decide who must have taken 8 years. Logical ordering and elimination will lead to the answer.

Step-by-Step Solution:
Step 1: Ravi took more time only than Raghu and completed in 5 years. The phrase more time only than Raghu means that among the four, Ravi took more time than exactly one person, Raghu, and less time than the other two.Step 2: Therefore, Raghu must have taken less time than 5 years. Since the minimum time is 3 years, and all times are distinct, Raghu must have taken 3 years.Step 3: We now know two of the times: Raghu = 3 years (minimum), Ravi = 5 years. The remaining two times for Rajesh and Ramesh must be greater than 5 years, with one of them equal to the maximum 8 years.Step 4: The statement that Ramesh did not take longer time than Rajesh means Ramesh took less than or equal to the time taken by Rajesh.Step 5: Since all times are distinct, less than or equal to here simplifies to strictly less than. So Ramesh took fewer years than Rajesh.Step 6: Because Rajesh took more time than Ramesh, and one of them must have taken the maximum of 8 years, it must be Rajesh who took 8 years.Step 7: The remaining time value between 5 and 8 (for example 6 or 7 years) would then belong to Ramesh, but the exact number is not needed for the question.

Verification / Alternative check:

Why Other Options Are Wrong:

• Ramesh cannot have taken the maximum time because he took fewer years than Rajesh.
• Raghu took the minimum time, 3 years, so he cannot be the slowest.
• Ravi took only 5 years and is faster than both Ramesh and Rajesh.
• None of these is incorrect because Rajesh fits all the conditions to be the one who took 8 years.

Common Pitfalls:

• Misreading the phrase more time only than Raghu and thinking Ravi is the slowest, which contradicts the data.
• Ignoring that all four time durations are distinct, which removes the possibility of ties.
• Confusing not longer than with strictly shorter in a context where all values must be different.

Final Answer:
The person who took the most years to complete graduation is Rajesh.