Vishal, Priyatham, Raghu, Karthik and Veeru are five friends. Vishal is twice as old as Priyatham. Raghu is half the age of Priyatham. Vishal is half the age of Veeru and Raghu is twice the age of Karthik. Based on these relationships, who is the youngest among the five friends?

Introduction / Context:
This is an age based reasoning question involving ratios and relative comparisons. The relationships between the ages of five people are given in terms of fractions and multiples. The task is to determine who is youngest, which means we must express all ages in terms of one base variable and then compare them.

Given Data / Assumptions:

• Let the age of Priyatham be P years.
• Vishal is twice as old as Priyatham, so Vishal is 2P.
• Raghu is half the age of Priyatham, so Raghu is P / 2.
• Vishal is half the age of Veeru, so Veeru is 2 times Vishal, that is 4P.
• Raghu is twice the age of Karthik, so Raghu = 2Karthik.

Concept / Approach:
We start by expressing all ages in terms of P, then solve for the age of Karthik using the relationship with Raghu. After we have expressions for each friend, we compare their numeric factors relative to P. The person with the smallest factor of P will be the youngest, because P itself is positive and common.

Step-by-Step Solution:
Step 1: Take Priyatham's age as P.Step 2: Vishal is twice Priyatham, so Vishal = 2P.Step 3: Raghu is half Priyatham, so Raghu = P / 2.Step 4: Vishal is half Veeru, so Veeru = 2 * Vishal = 4P.Step 5: Raghu is twice Karthik, so P / 2 = 2 * Karthik, which implies Karthik = P / 4.Step 6: Now we have ages: Priyatham = P, Vishal = 2P, Raghu = P / 2, Veeru = 4P, and Karthik = P / 4.Step 7: Compare the multiples and fractions: P / 4, P / 2, P, 2P, 4P. The smallest value is P / 4.Step 8: Therefore, Karthik, with age P / 4, is the youngest.

Verification / Alternative check:
We can imagine a simple numeric example. Let P = 4 years for convenience. Then Vishal is 8, Raghu is 2, Veeru is 16, and Karthik is 1 year old. Comparing 4, 8, 2, 16 and 1 clearly shows that Karthik is the youngest. This numeric substitution confirms our algebraic conclusion.

Why Other Options Are Wrong:
Veeru has the largest age factor 4P, making him the oldest, not the youngest. Vishal is 2P, which is double Priyatham and also older. Raghu is P / 2, which is older than P / 4. Therefore, options A, C, and D do not represent the youngest friend.

Common Pitfalls:
Some learners stop after identifying that Raghu is half of Priyatham and think he might be the youngest, forgetting that Karthik is related to Raghu by another halving. Another error is mixing up half and double relationships, especially when several are chained. Writing all ages in terms of a single variable P is the safest method.

Final Answer:
The youngest among the five friends is Karthik.