Study the following information carefully and answer the questions given below:

Six persons i.e., R, T, P, U, S and Q travel to the different states i.e., Delhi, Sikkim, Odisha, Goa, Kerala and Assam on two different dates i.e., 9 th and 26 th of three different months viz. May, June and July of the same year but not necessarily in the same order.

One person travel between P and the person who travels to Delhi. The person who travels to Delhi neither travels in month having an even number of days nor on even date. The person who travels to Delhi and the person who travels to Goa is not the first person to travel. Two Person travels between T and U who travels to Goa. T travels after P. The person who travels to Odisha travels just before S. Two persons travel between the person who travels to Kerala and the person who travels to Assam. U does not travel just after the person who travels to Assam. The number of persons travel between Q and S is one more than the number of person travel before R.

Which of the following combination(s) is/are correct?

The correct answer is S - Assam.

Step-by-Step Explanation:

1. Identify the given parameters and dates:

There are 6 persons (R, T, P, U, S, Q) traveling to 6 different states (Delhi, Sikkim, Odisha, Goa, Kerala, Assam) across 3 months (May, June, July) on 2 dates each (9th, 26th):

1. May 9th (31 days, odd date)

2. May 26th (31 days, even date)

3. June 9th (30 days, odd date)

4. June 26th (30 days, even date)

5. July 9th (31 days, odd date)

6. July 26th (31 days, even date)

2. Decode the clues step-by-step:

• "The person who travels to Delhi neither travels in month having an even number of days nor on even date."
June has 30 days (even). So Delhi must be in May or July. The date must be an odd date (9th). Thus, Delhi can be on May 9th or July 9th.

• "The person who travels to Delhi and the person who travels to Goa is not the first person to travel."
May 9th is the 1st position (first person to travel). Therefore, the person traveling to Delhi cannot travel on May 9th.
Hence, Delhi = July 9th (5th position).

• "One person travel between P and the person who travels to Delhi."
Delhi is at 5th position (July 9th). So P can be at 3rd position (June 9th).

• "T travels after P." and "Two Person travels between T and U who travels to Goa."
Position of P = 3rd (June 9th).
T travels after P, so T can be at 4th (June 26th) or 6th (July 26th).
- If T is at 4th (June 26th), then U (who travels to Goa) must be 2 persons away from T. U could be at 1st position (May 9th). But we know Goa is not the first person to travel! So T cannot be at 4th.
- Therefore, T = July 26th (6th position).
- Since 2 persons travel between T and U, U (Goa) = June 9th (3rd position)... wait, P is at 3rd position! Let's re-verify:

If Delhi is at 5th position (July 9th):
- 1 person between P and Delhi: P could be 3rd (June 9th) or P could be... wait, 1 person between P and 5th means P is at 3rd (June 9th) or 7th (not possible). So P = June 9th.
- U (Goa) is 2 persons away from T.
- T is after P (June 9th). If T = July 26th (6th), then U (Goa) is 2 persons before T, which is 3rd position (June 9th). But P is at 3rd! Contradiction?
Let's check: 2 persons between T and U. Positions: 1, 2, 3, 4, 5, 6.
If T = 6th, 2 persons between them means U is at 3rd (6 - 3 = 3rd? No, between 3rd and 6th are 4th and 5th, so 2 persons!).
Wait! If P is at 3rd, U can't be at 3rd.
Let's re-evaluate: "One person travel between P and the person who travels to Delhi."
Positions: 1 (May 9), 2 (May 26), 3 (June 9), 4 (June 26), 5 (July 9), 6 (July 26).
If Delhi = 5th (July 9):
1 person between P and Delhi means P is at 3rd (June 9).
If P = 3rd, T > P (so T is 4th, 5th, or 6th).
- If T = 4th, U = 1st (not allowed since Goa is not 1st) or U = 7th (impossible).
- If T = 5th (Delhi), then U = 2nd (May 26). U travels to Goa!
- If T = 6th, U = 3rd (conflict with P = 3rd).
So, T = July 9th (Delhi) and U (Goa) = May 26th!

3. Summary of schedule so far:
1. May 9th: [ Person , State ]
2. May 26th: [ U , Goa ]
3. June 9th: [ P , State ]
4. June 26th: [ Person , State ]
5. July 9th: [ T , Delhi ]
6. July 26th: [ Person , State ]

• "The person who travels to Odisha travels just before S."
Odisha and S are consecutive: [Odisha, S].
• "The number of persons travel between Q and S is one more than the number of person travel before R."
Let number of persons before R be $x$. Then number of persons between Q and S is $x\; +\; 1$.
Since total persons = 6:
- If R is at 1st position (May 9), persons before R = 0.
Then persons between Q and S = $0\; +\; 1\; =\; 1$.
If R = 1st, remaining open positions for persons are 4th (June 26), 6th (July 26).
So Q and S must be at 4th and 6th, or 1st and 3rd... but R is at 1st, P is at 3rd, U is at 2nd, T is at 5th!
Therefore, the person positions filled so far are:
2nd = U, 3rd = P, 5th = T.
Open positions for R, Q, S are 1st, 4th, 6th!

Let's place R, Q, S in {1st, 4th, 6th}:
- If R = 1st position (May 9), persons before R = 0.
Then between Q and S there is $0\; +\; 1\; =\; 1$ person.
Since open positions for Q and S are 4th and 6th, the persons between 4th and 6th is 1 person (5th, which is T). This matches perfectly!
So Q and S are at 4th and 6th positions, and R = May 9th (1st position).

Now determine which is S (4th or 6th):
- We know [Odisha, S], meaning S must have a state directly before it.
- If S = 4th (June 26), the person just before S is 3rd (June 9, which is P). So P travels to Odisha.
- If S = 6th (July 26), the person just before S is 5th (July 9, which is T = Delhi). So T travels to Odisha, but T travels to Delhi! Contradiction.
Therefore, S = June 26th (4th position) and Q = July 26th (6th position).
And P (3rd position) = Odisha.

4. Completing the remaining States:
Current Person & State mappings:
1. May 9th: R - [State]
2. May 26th: U - Goa
3. June 9th: P - Odisha
4. June 26th: S - [State]
5. July 9th: T - Delhi
6. July 26th: Q - [State]

Remaining states to assign: Kerala, Assam, Sikkim.
• "Two persons travel between the person who travels to Kerala and the person who travels to Assam."
The available state positions are 1st, 4th, and 6th.
The gap of 2 persons between Kerala and Assam means they must be at 1st and 4th positions (since between 1st and 4th are 2nd and 3rd, i.e., 2 persons!).
So Kerala and Assam are at 1st (May 9) and 4th (June 26).

• "U does not travel just after the person who travels to Assam."
U is at 2nd position (May 26). The position just before U is 1st position (May 9).
Since U does not travel just after Assam, Assam cannot be at 1st position (May 9).
Therefore:
- 1st position (R) = Kerala
- 4th position (S) = Assam
- 6th position (Q) = Sikkim (remaining state)

Final Arrangement:

1. May 9th: R - Kerala
2. May 26th: U - Goa
3. June 9th: P - Odisha
4. June 26th: S - Assam
5. July 9th: T - Delhi
6. July 26th: Q - Sikkim

Checking the option "S - Assam": S travels to Assam on June 26th, which is correct.