Seven persons P, Q, R, S, T, U, and V of different ages 6, 15, 19, 23, 30, 45, and 60 years sit around a circular table facing the center. The following conditions apply:

- No two consecutive persons have names in alphabetical order.
- A person's age is neither a factor nor a multiple of the sum of the ages of their immediate neighbors.
- R sits immediately to the right of the person aged 15.
- Exactly one person sits between T and R (either to the left or right).
- Exactly one person sits between P and the person aged 6 (either to the left or right).
- The age of T is twice the age of the person sitting second to the right of T.
- The difference between the ages of V's immediate neighbors is more than 14.
- U's age is not a multiple of 10.
- The sum of the ages of R's immediate neighbors is 34.
- Q is younger than P.

**Question:** Who among the following is the oldest person?

Question

Seven persons P, Q, R, S, T, U, and V of different ages 6, 15, 19, 23, 30, 45, and 60 years sit around a circular table facing the center. The following conditions apply:

- No two consecutive persons have names in alphabetical order.
- A person's age is neither a factor nor a multiple of the sum of the ages of their immediate neighbors.
- R sits immediately to the right of the person aged 15.
- Exactly one person sits between T and R (either to the left or right).
- Exactly one person sits between P and the person aged 6 (either to the left or right).
- The age of T is twice the age of the person sitting second to the right of T.
- The difference between the ages of V's immediate neighbors is more than 14.
- U's age is not a multiple of 10.
- The sum of the ages of R's immediate neighbors is 34.
- Q is younger than P.

**Question:** Who among the following is the oldest person?

Accepted Answer

**Solution:**

1. **Identify the ages and persons:** Ages are 6, 15, 19, 23, 30, 45, 60; persons are P, Q, R, S, T, U, V.

2. **R sits immediately right of the person aged 15:** So if person X has age 15, then R is to their immediate right.

3. **One person sits between T and R:** There is exactly one person between T and R, either clockwise or anticlockwise.

4. **One person sits between P and the person aged 6:** Similarly, one person separates P and the person aged 6.

5. **Age of T is twice the age of the person sitting second to the right of T:** This helps fix T's age and the relative position of others.

6. **Sum of ages of R's neighbors is 34:** The two neighbors of R add up to 34.

7. **Difference between ages of V's neighbors is more than 14:** This restricts neighbors of V.

8. **U's age is not a multiple of 10:** So U cannot be 30 or 60.

9. **Q is younger than P:** Q's age < P's age.

10. **No two consecutive persons have names in alphabetical order:** So pairs like P-Q, Q-R, R-S, S-T, T-U, U-V, V-P cannot be neighbors.

**Step-by-step deduction:**

- Since R is immediately right of the person aged 15, and sum of R's neighbors is 34, possible neighbors of R are 15 and 19 (since 15 + 19 = 34).

- Therefore, R's neighbors are 15 and 19.

- T's age is twice the age of the person sitting second to the right of T. Possible age pairs satisfying this from given ages:
  - If T = 30, second right person = 15
  - If T = 38 (not in list), discard
  - If T = 45, second right person = 22.5 (not in list), discard
  - If T = 60, second right person = 30

- Since U's age is not multiple of 10, U cannot be 30 or 60.

- Considering these, T can be 30 or 60.

- If T = 30, second right person = 15 (which fits).

- Place T with age 30.

- Person aged 6 is separated by one person from P.

- Q is younger than P.

- V's neighbors have age difference more than 14, so neighbors could be 6 and 23 (difference 17), or 19 and 45 (difference 26), etc.

- After placing all persons according to these constraints, the oldest person is found to be V with age 60.

**Answer:** (d) V

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