Nine individuals P, Q, R, S, T, U, V, W, and X belong to three different states: Assam, Manipur, and Tripura. Each state has at least two and at most four persons. The following conditions apply:

- If a person A and the one who is 12 years old belong to the same state, then A is not 12 years old.
- W and the person aged 51 belong to the same state.
- Only Q and the person aged 18 belong to the same state.
- P and V belong to different states.
- W is 7 years younger than V.
- S is twice as old as Q.
- P and S belong to different states.
- V is 61 years old, and the person aged 64 belongs to the same state as V.
- S does not belong to Assam or Tripura.
- The person aged 35 belongs to Tripura.
- No one's age is less than 18 or more than 68.
- T and the person aged 64 belong to the same state.
- W does not belong to Tripura.
- U and the person aged 29 belong to the same state.
- P does not belong to Assam.
- R is 29 years old and is 3 years younger than Q.
- X is the youngest.
- P is 2 years older than U.
- P's age is not a multiple of 5.

Based on the above, what is the sum of the ages of T, P, and W?

Question

Nine individuals P, Q, R, S, T, U, V, W, and X belong to three different states: Assam, Manipur, and Tripura. Each state has at least two and at most four persons. The following conditions apply:

- If a person A and the one who is 12 years old belong to the same state, then A is not 12 years old.
- W and the person aged 51 belong to the same state.
- Only Q and the person aged 18 belong to the same state.
- P and V belong to different states.
- W is 7 years younger than V.
- S is twice as old as Q.
- P and S belong to different states.
- V is 61 years old, and the person aged 64 belongs to the same state as V.
- S does not belong to Assam or Tripura.
- The person aged 35 belongs to Tripura.
- No one's age is less than 18 or more than 68.
- T and the person aged 64 belong to the same state.
- W does not belong to Tripura.
- U and the person aged 29 belong to the same state.
- P does not belong to Assam.
- R is 29 years old and is 3 years younger than Q.
- X is the youngest.
- P is 2 years older than U.
- P's age is not a multiple of 5.

Based on the above, what is the sum of the ages of T, P, and W?

Accepted Answer

**Solution:**

1. From the conditions, we start by identifying ages:
   - X is the youngest and only Q and the person aged 18 belong to the same state, so X is 18 years old.
   - R is 29 years old and 3 years younger than Q, so Q is 32 years old.
   - S is twice as old as Q, so S is 64 years old.
   - V is 61 years old.
   - W is 7 years younger than V, so W is 54 years old.
   - The person aged 35 belongs to Tripura.
   - U and the person aged 29 belong to the same state, so U is 35 years old (since R is 29 and belongs to Tripura).
   - P is 2 years older than U, so P is 37 years old.

2. Assigning states:
   - S is not from Assam or Tripura, so S belongs to Manipur.
   - V (61), S (64), T (51), and W (54) belong to the same state (Manipur).
   - R (29), P (37), and U (35) belong to Tripura.
   - Q (32) and X (18) belong to Assam.

3. Now, sum the ages of T, P, and W:
   - T is 51 years old.
   - P is 37 years old.
   - W is 54 years old.

4. Calculate the sum:
   $$51 + 37 + 54 = 142$$

**Answer:** 142 years

Answer

Answer

Answer