The correct option is Only II.
Step-by-step Explanation:
Step 1: Understand the given dates and months
There are 4 months: August (31 days), October (31 days), November (30 days), and December (31 days).
Each month has two dates: 11th and 20th.
This gives a total of 8 sequential positions:
1. 11th August
2. 20th August
3. 11th October
4. 20th October
5. 11th November (Month with even number of days)
6. 20th November (Month with even number of days)
7. 11th December
8. 20th December
Step 2: Determine the positions of the persons using the given clues
1. B was born in the month having even number of days (November). So, B could be born on 11th November (Position 5) or 20th November (Position 6).
2. G was born four persons before B:
- If B is at Position 5, G would be at Position 5 - 4 = 1.
- If B is at Position 6, G would be at Position 6 - 4 = 2.
3. E was born two persons after G:
- If G is at Position 1, E would be at Position 1 + 2 = 3.
- If G is at Position 2, E would be at Position 2 + 2 = 4.
4. A was born three persons before E:
- If E is at Position 3, A would be at Position 3 - 3 = 0, which is invalid.
- If E is at Position 4, A would be at Position 4 - 3 = 1. This is valid.
Hence, the fixed positions so far are:
- Position 1 (11th Aug): A
- Position 2 (20th Aug): G
- Position 4 (20th Oct): E
- Position 6 (20th Nov): B
5. F was born in the month having an even number of days (November):
Since Position 6 (20th Nov) is occupied by B, F must be at Position 5 (11th Nov).
6. F was born after C:
Since F is at Position 5, C must be placed at the remaining available spot before Position 5, which is Position 3 (11th Oct).
7. D was born on an odd number date:
The remaining positions are Position 7 (11th Dec) and Position 8 (20th Dec). Since 11 is an odd date, D must be born on 11th December (Position 7).
8. Remaining Person (H):
H is placed at the final remaining spot, Position 8 (20th Dec).
Final Seating / Birth Order:
1. 11th August: A
2. 20th August: G
3. 11th October: C
4. 20th October: E
5. 11th November: F
6. 20th November: B
7. 11th December: D
8. 20th December: H
Step 3: Evaluate the given statements
Statement I: D was born on 11th December.
- D was indeed born on 11th December (Position 7). This statement is Correct.
Statement II: As many persons were born before G as after H.
- Number of persons born before G (Position 2) = 1 (A).
- Number of persons born after H (Position 8) = 0.
Since 1 ≠ 0, this statement is Incorrect.
Statement III: E was born three persons before D.
- Position of D is 7. Three persons before D is Position 7 - 3 = 4, which is E. This statement is Correct.
Therefore, Only II is the incorrect statement.