Eight persons — A, B, C, D, E, F, G and H were studying about different birds in different months of the same year, viz. January, March, May, June, July, October, November and December, but not necessarily in the same order. Each of them is studying about different birds — Kingfisher, Toucans, Penguin, Ostrich, Woodpecker, Loon, Sparrow and Peacock.

G is studying in the month having odd number of days. Either two persons were studying before G or after G. Two persons were studying between G and the one who is studying about loon. H was studying three persons after the person who is studying about ostrich and four months before A. Three persons were studying between A and the one who is studying about Woodpecker. B is studying about Sparrow two persons before F. F is studying before E. The one who is studying about Penguin is studying immediately after the one studying about Kingfisher. Two persons were studying between the ones studying about Kingfisher and Peacock. D is not the first one to study.

Which among the following statement is not true?
I. A is studying about Loon
II. F is studying in the month having even number of days.
III. C is studying in the month after D.

The correct option is Only III.

Let's systematically solve the puzzle step-by-step to find the arrangement of the eight persons, the months they studied in, and the birds they studied. Then we will verify each statement to find the one that is not true.

First, let's list the months and the number of days in each:
1. January (31 days - Odd)
2. March (31 days - Odd)
3. May (31 days - Odd)
4. June (30 days - Even)
5. July (31 days - Odd)
6. October (31 days - Odd)
7. November (30 days - Even)
8. December (31 days - Odd)

Let's analyze the clues:
1. G studied in a month with an odd number of days (January, March, May, July, October, December).
2. Either two persons studied before G or two persons studied after G.
This means G is either 3rd (May) or 6th (October).
Case 1: G is in May.
Case 2: G is in October.
Since May and October both have 31 days (odd number of days), both cases are possible.

3. Two persons studied between G and the one studying about Loon.
In Case 1 (G is 3rd): The one studying about Loon is either 6th (October) or 8th (no, 3rd + 3 = 6th, so 2 persons between means 3rd and 6th). Thus, the Loon student is 6th (October).
In Case 2 (G is 6th): The one studying about Loon is 3rd (May).

4. H studied three persons after the one studying about Ostrich. This means: Ostrich, _, _, H (H is 3 persons after Ostrich).
5. H studied four months before A.
Let's look at the months gap:
If H is in January (Month 1): A must be in January + 4 months = May (Month 3).
If H is in March (Month 2): A must be in March + 4 months = July (Month 5).
If H is in June (Month 4): A must be in June + 4 months = October (Month 6).
If H is in July (Month 5): A must be in July + 4 months = November (Month 7).

6. Three persons studied between A and the one studying about Woodpecker.
7. B is studying about Sparrow two persons before F (B, _, F).
8. F is studying before E.
9. Kingfisher is immediately followed by Penguin (Kingfisher, then Penguin).
10. Two persons studied between Kingfisher and Peacock.
11. D is not the first one to study.

Let's test Case 1: G is in May (3rd). Loon is in October (6th).
Now let's check the H and A relationship (H is four months before A):
- If H is in January (1st), A is in May (3rd). But G is in May (3rd), which is a conflict.
- If H is in March (2nd), A is in July (5th).
Let's check if H is 2nd (March) and A is 5th (July):
Ostrich must be 3 persons before H, but H is 2nd, so Ostrich would have to be in a position before 1st, which is impossible.
- If H is in June (4th), A is in October (6th). But Loon is in October (6th), which is fine (A can study Loon).
Since H is 4th (June), Ostrich must be 3 persons before H, which is 1st (January).
So:
1. January: Ostrich
2. March:
3. May: G
4. June: H
5. July:
6. October: A (Loon)
7. November:
8. December:
Let's check the condition: Three persons studied between A (6th) and Woodpecker.
Positions between 6th and Woodpecker: Woodpecker must be 2nd (March) (since 6 - 3 - 1 = 2).
So:
2. March: Woodpecker
Now we have:
1. January: Ostrich
2. March: Woodpecker
3. May: G
4. June: H
5. July:
6. October: A (Loon)
7. November:
8. December:

Now let's place B (Sparrow) and F (B is two persons before F, i.e., B, [person], F):
- If B is 3rd (May), F is 5th (July). But G is 3rd.
- If B is 5th (July), F is 7th (November). This is possible.
Let's try: B (Sparrow) is 5th (July), and F is 7th (November).
Then, F is before E. So E must be 8th (December).
This leaves position 2 (March) and position 1 (January) and position 4 (June) and position 8 (December) for other persons.
We have persons: A, B, C, D, E, F, G, H.
Currently placed: G (3rd), H (4th), B (5th), A (6th), F (7th), E (8th).
Remaining persons: C and D.
Since D is not the first one to study, D cannot be 1st (January). Thus, D must be 2nd (March), and C must be 1st (January).
Let's check the table of persons:
1. January: C (Ostrich)
2. March: D (Woodpecker)
3. May: G
4. June: H
5. July: B (Sparrow)
6. October: A (Loon)
7. November: F
8. December: E

Now let's place the remaining birds: Kingfisher, Penguin, Peacock, Toucans.
- The one studying about Penguin is studying immediately after the one studying about Kingfisher.
- Two persons studied between the ones studying about Kingfisher and Peacock.
Let's find consecutive positions for Kingfisher and Penguin:
Possible consecutive empty bird slots:
- 3rd (May) and 4th (June)
- 7th (November) and 8th (December)
Sub-case A: Kingfisher is 3rd (May) and Penguin is 4th (June).
Then, Peacock must be two persons away from Kingfisher (3rd), which means Peacock is 6th (October) or 8th (no, 3rd + 2 + 1 = 6th, or 3rd - 2 - 1 = 0). So Peacock must be 6th (October). But 6th is already Loon. So this is invalid.
Sub-case B: Kingfisher is 7th (November) and Penguin is 8th (December).
Then Peacock must be two persons away from Kingfisher (7th), which means Peacock is 4th (June) (since 7 - 2 - 1 = 4).
This fits perfectly!
So:
4. June: H (Peacock)
7. November: F (Kingfisher)
8. December: E (Penguin)
The remaining bird is Toucans, which must be assigned to G (3rd, May).

Let's write down the final complete arrangement:
1. January: C (Ostrich)
2. March: D (Woodpecker)
3. May: G (Toucans)
4. June: H (Peacock)
5. July: B (Sparrow)
6. October: A (Loon)
7. November: F (Kingfisher)
8. December: E (Penguin)

Now let's check the given statements:
I. A is studying about Loon
Looking at our table, A is indeed studying about Loon in October. This statement is TRUE.

II. F is studying in the month having even number of days.
F is studying in November, which has 30 days (even number of days). This statement is TRUE.

III. C is studying in the month after D.
C is studying in January, while D is studying in March. Therefore, C is studying in the month before D, not after. This statement is NOT TRUE.

Since only statement III is not true, the correct option is Only III.