Given: Nine persons, namely, C, E, G, I, K, M, O, Q, and S, are scheduled to visit 9 different cities, viz, Agra, Aligarh, Delhi, Morena, Bangalore, Meerut, Chennai, Jabalpur, and Ajmer, but not necessarily in the same order. They travel on three different dates, 7, 14, and 28, across three different months, namely, January, April, and October, but not necessarily in the same order.
1. G travels on an even date in April.
Here, we have 2 Cases, i.e., Case 1 and Case 2.
| Months | Dates | Persons - City | |
|---|
| Case 1 | Case 2 | | |
| January (31) | 7 | | |
| 14 | | |
| 28 | | |
| April (30) | 7 | | |
| 14 | G - | |
| 28 | | G - |
| October (31) | 7 | | |
| 14 | | |
| 28 | | |
- Three people travel between G and the one who goes to Chennai.
| Months | Dates | Persons - City | |
|---|
| Case 1 | Case 2 | | |
| January (31) | 7 | - Chennai/ | |
| 14 | | - Chennai |
| 28 | | |
| April (30) | 7 | | |
| 14 | G - | |
| 28 | | G - |
| October (31) | 7 | | |
| 14 | | |
| 28 | - Chennai/ | |
- M travels immediately before the person visiting Chennai.
| Months | Dates | Persons - City | |
|---|
| Case 1 | Case 2 | | |
| January (31) | 7 | | M - |
| 14 | | - Chennai |
| 28 | | |
| April (30) | 7 | | |
| 14 | G - | |
| 28 | | G - |
| October (31) | 7 | | |
| 14 | M - | |
| 28 | - Chennai | |
- Five people travel between M and C.
| Months | Dates | Persons - City | |
|---|
| Case 1 | Case 2 | | |
| January (31) | 7 | | M - |
| 14 | C - | - Chennai |
| 28 | | |
| April (30) | 7 | | |
| 14 | G - | |
| 28 | | G - |
| October (31) | 7 | | C - |
| 14 | M - | |
| 28 | - Chennai | |
5. The number of people who travel before C is equal to the number who travel after the one visiting Meerut.
| Months | Dates | Persons - City | |
|---|
| Case 1 | Case 2 | | |
| January (31) | 7 | | M - |
| 14 | C - | - Chennai |
| 28 | | - Meerut |
| April (30) | 7 | | |
| 14 | G - | |
| 28 | | G - |
| October (31) | 7 | | C - |
| 14 | M - Meerut | |
| 28 | - Chennai | |
6. Four people travel between S and the one who goes to Meerut.
| Months | Dates | Persons - City | |
|---|
| Case 1 | Case 2 | | |
| January (31) | 7 | | M - |
| 14 | C - | - Chennai |
| 28 | S - | - Meerut |
| April (30) | 7 | | |
| 14 | G - | |
| 28 | | G - |
| October (31) | 7 | | C - |
| 14 | M - Meerut | S - |
| 28 | - Chennai | |
- C and Q travel in the same month.
| Months | Dates | Persons - City | |
|---|
| Case 1 | Case 2 | | |
| January (31) | 7 | Q - | M - |
| 14 | C - | - Chennai |
| 28 | S - | - Meerut |
| April (30) | 7 | | |
| 14 | G - | |
| 28 | | G - |
| October (31) | 7 | | C - |
| 14 | M - Meerut | S - |
| 28 | - Chennai | Q - |
8. M does not go to Delhi.
9. O travels immediately after the person who visits Delhi.
Here, we have 2 more subcases of Case 1, i.e., Case 1a and Case 1b.
| Months | Dates | Persons - City | | | |
|---|
| Case 1 | Case 1a | Case 1b | Case 2 | | |
| January (31) | 7 | Q - | Q - | Q - | M - |
| 14 | C - | C - | C - | - Chennai |
| 28 | S - Delhi | S - | S - | - Meerut |
| April (30) | 7 | O - | | | - Delhi |
| 14 | G - | G - Delhi | G - | O - |
| 28 | | O - | - Delhi | G - |
| October (31) | 7 | | | O - | C - |
| 14 | M - Meerut | M - Meerut | M - Meerut | S - |
| 28 | - Chennai | - Chennai | - Chennai | Q - |
10. Three people travel between O and the one who visits Jabalpur.
Now, we can eliminate Case 1 (Because there is no place for the one who visits Jabalpur.)
| Months | Dates | Persons - City | | |
|---|
| Case 1a | Case 1b | Case 2 | | |
| January (31) | 7 | Q - | Q - | M - Jabalpur/ |
| 14 | C - Jabalpur | C - | - Chennai |
| 28 | S - | S - Jabalpur | - Meerut |
| April (30) | 7 | | | - Delhi |
| 14 | G - Delhi | G - | O - |
| 28 | O - | - Delhi | G - |
| October (31) | 7 | | O - | C - |
| 14 | M - Meerut | M - Meerut | S - |
| 28 | - Chennai | - Chennai | Q - Jabalpur/ |
- One person travels between those who go to Jabalpur and Aligarh.
| Months | Dates | Persons - City | | |
|---|
| Case 1a | Case 1b | Case 2 | | |
| January (31) | 7 | Q - | Q - Aligarh/ | M - |
| 14 | C - Jabalpur | C - | - Chennai |
| 28 | S - | S - Jabalpur | - Meerut |
| April (30) | 7 | - Aligarh | | - Delhi |
| 14 | G - Delhi | G - Aligarh/ | O - |
| 28 | O - | - Delhi | G - |
| October (31) | 7 | | O - | C - Aligarh |
| 14 | M - Meerut | M - Meerut | S - |
| 28 | - Chennai | - Chennai | Q - Jabalpur |
12. The person visiting Morena travels just before the one going to Bangalore.
Now, we have 1 more subcase of Case 1b, i.e., Case 1b(i).
| Months | Dates | Persons - City | | | |
|---|
| Case 1a | Case 1b | Case 1b(i) | Case 2 | | |
| January (31) | 7 | Q - | Q - Aligarh | Q - Morena | M - |
| 14 | C - Jabalpur | C - | C - Bangalore | - Chennai |
| 28 | S - | S - Jabalpur | S - Jabalpur | - Meerut |
| April (30) | 7 | - Aligarh | - Morena | | - Delhi |
| 14 | G - Delhi | G - Bangalore | G - Aligarh | O - Morena |
| 28 | O - Morena | - Delhi | - Delhi | G - Bangalore |
| October (31) | 7 | - Bangalore | O - | O - | C - Aligarh |
| 14 | M - Meerut | M - Meerut | M - Meerut | S - |
| 28 | - Chennai | - Chennai | - Chennai | Q - Jabalpur |
- One person travels between K and the one who goes to Agra.
Now, we can eliminate Case 1a.
| Months | Dates | Persons - City | | |
|---|
| Case 1b | Case 1b(i) | Case 2 | | |
| January (31) | 7 | Q - Aligarh | Q - Morena | M - Agra |
| 14 | C - Agra/ | C - Bangalore | - Chennai |
| 28 | S - Jabalpur | S - Jabalpur | K - Meerut |
| April (30) | 7 | K/ - Morena | - Agra/ | - Delhi |
| 14 | G - Bangalore | G - Aligarh | O - Morena |
| 28 | - Delhi | K/ - Delhi | G - Bangalore |
| October (31) | 7 | O - Agra/ | O - Agra/ | C - Aligarh |
| 14 | M - Meerut | M - Meerut | S - |
| 28 | K/ - Chennai | K/ - Chennai | Q - Jabalpur |
- E travels immediately after K.
Now, we can eliminate Case 1b and Case 1b(i).
| Months | Dates | Persons - City |
|---|
| Case 2 | | |
| January (31) | 7 | M - Agra |
| 14 | - Chennai |
| 28 | K - Meerut |
| April (30) | 7 | E - Delhi |
| 14 | O - Morena |
| 28 | G - Bangalore |
| October (31) | 7 | C - Aligarh |
| 14 | S - |
| 28 | Q - Jabalpur |
This is our final arrangement,
| Months | Dates | Persons - City |
|---|
| Case 2 | | |
| January (31) | 7 | M - Agra |
| 14 | I - Chennai |
| 28 | K - Meerut |
| April (30) | 7 | E - Delhi |
| 14 | O - Morena |
| 28 | G - Bangalore |
| October (31) | 7 | C - Aligarh |
| 14 | S - Ajmer |
| 28 | Q - Jabalpur |
I. C goes to Aligarh : True
II. M travels before I : True
III. S travels on 14th October : True
Hence, the correct answer is All I, II, and III are correct.