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.

Who among the following person travels to Sikkim?

The correct option is Q.

Step-by-Step Explanation:

Let's analyze the given information step-by-step to determine the schedule for the six persons (R, T, P, U, S, Q) traveling to six different states (Delhi, Sikkim, Odisha, Goa, Kerala, Assam) on two dates (9th and 26th) of three months (May, June, July):

1. Dates and Months Layout:

The available slots in chronological order are:

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. Placing the person who travels to Delhi:

- "The person who travels to Delhi neither travels in a month having an even number of days nor on an even date."

- Months with odd number of days (31 days) are May and July.

- Odd dates are 9th.

- So Delhi can be on May 9th or July 9th.

- However, "The person who travels to Delhi and the person who travels to Goa is not the first person to travel." This means Delhi cannot be on May 9th (the 1st slot).

- Therefore, the person traveling to Delhi MUST travel on July 9th.

3. Placing P:

- "One person travels between P and the person who travels to Delhi."

- Since Delhi is on July 9th (5th slot), P must be on June 9th (3rd slot).

4. Placing T, U, and Goa:

- "T travels after P." (P is on June 9th, so T is after June 9th).

- "Two persons travel between T and U who travels to Goa."

- U travels to Goa.

- If T is on July 26th (6th slot), then U (Goa) would be on June 9th, but P is already on June 9th.

- If T is on June 26th (4th slot), then U (Goa) must be on May 9th (1st slot). But Goa cannot be the first person to travel! So this is invalid.

- If T is on July 9th (5th slot), but Delhi is already on July 9th. Wait, P is on June 9th (3rd slot). "Two persons travel between T and U".

- Let's re-evaluate: If U (Goa) is on June 26th (4th slot), then T could be on May 9th (1st slot), but T travels after P (June 9th), so T cannot be on May 9th.

- If U (Goa) is on July 26th (6th slot), then T must be on June 9th, but P is on June 9th. Wait! Two persons between T and U means if U is 6th, T is 3rd (already P). If U is 5th (Delhi), no, U goes to Goa. If U is 4th (June 26th), T would be 1st (May 9th), but T is after P.

- Let's re-check P and Delhi: "One person travel between P and the person who travels to Delhi."

- Since Delhi is on July 9th (5th slot), P can also be on July 26th (6th slot)? No, between slot 5 and slot 6 there are 0 persons. Between slot 5 and slot 3 there is 1 person (slot 4). So P is definitely on June 9th (3rd slot).

- Since T travels after P (June 9th), T can be on June 26th (4th), July 9th (5th), or July 26th (6th).

- If T is on July 26th (6th), 2 persons between T and U means U is on June 9th (3rd slot), but P is on June 9th. Contradiction.

- If T is on June 26th (4th), 2 persons between T and U means U is on May 9th (1st slot), but Goa cannot be 1st. Contradiction.

- Therefore, U must be on July 26th (6th slot), and T is on June 26th? Wait, between slot 6 and slot 3 there are 2 persons (slots 4 and 5)! So T can be on June 9th? No, P is on June 9th.

- Let's re-read: "Two persons travel between T and U who travels to Goa."

- What if T is on May 26th (2nd slot) and U is on July 9th? But Delhi is on July 9th, and U travels to Goa. Also T is after P.

- Ah! What if T is on July 26th (6th slot) and U is on May 26th (2nd slot)? Two persons (slots 3, 4, 5 - wait, between 2nd and 6th there are 3 persons). Between 2nd and 5th there are 2 persons (3rd and 4th). If U (Goa) is on May 26th (2nd slot), then T is on July 9th (5th slot)? But Delhi is on July 9th! So T cannot be on July 9th unless T is the person who travels to Delhi!

- Yes! T travels to Delhi on July 9th! Let's check:

- Delhi = T (July 9th, 5th slot)

- U (Goa) = May 26th (2nd slot)

- Persons between U (2nd) and T (5th) = 2 persons (3rd and 4th slots). This matches perfectly!

- T (July 9th) travels after P (June 9th). This also matches!

5. Placing Odisha and S:

- "The person who travels to Odisha travels just before S."

- The available slots for S and Odisha (consecutive slots):

- May 9th & May 26th (U is on May 26th, so no)

- June 9th & June 26th (P is on June 9th, so Odisha = June 9th / P, S = June 26th)

- July 9th & July 26th (T/Delhi is on July 9th, so no)

- Thus, P (June 9th) travels to Odisha, and S travels on June 26th.

6. Placing R and Q:

- Slots remaining for persons: May 9th (1st slot) and July 26th (6th slot).

- "The number of persons travel between Q and S is one more than the number of person travel before R."

- S is on June 26th (4th slot).

- If R is on May 9th (1st slot), persons before R = 0. Then persons between Q and S must be 0 + 1 = 1. If Q is on July 26th (6th slot), persons between Q (6th) and S (4th) is 1 (the 5th slot, July 9th)! This matches!

- So R travels on May 9th and Q travels on July 26th.

7. Determining remaining states (Sikkim, Kerala, Assam):

- "Two persons travel between the person who travels to Kerala and the person who travels to Assam."

- Slots: 1st (May 9th), 3rd (June 9th = Odisha), 4th (June 26th), 5th (July 9th = Delhi), 6th (July 26th = Goa).

- The two state slots with 2 persons between them must be 1st (May 9th) and 4th (June 26th).

- So Kerala and Assam are on May 9th and June 26th.

- "U (May 26th) does not travel just after the person who travels to Assam."

- Since U is on May 26th (2nd slot), the person just before U is on May 9th (1st slot). So May 9th CANNOT be Assam.

- Therefore, May 9th (R) = Kerala, and June 26th (S) = Assam.

- The only remaining state is Sikkim, which must be assigned to July 26th (Q).

Final Schedule Summary:

- May 9th: R (Kerala)

- May 26th: U (Goa)

- June 9th: P (Odisha)

- June 26th: S (Assam)

- July 9th: T (Delhi)

- July 26th: Q (Sikkim)

Therefore, Q is the person who travels to Sikkim.