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

Six persons – A, B, C, D, E and F – were born in different months – April, July, and September – on two different dates, i.e., 9th and 26th of the same year. Each person likes a different colour – Red, Blue, Pink, Green, White, and Yellow. All the information is not necessarily used in the same order

Two persons were born between F and the person who likes red. D was born immediately before F on an odd date and in the month having even number of days. The one who likes pink was born two persons before C. E was born immediately before C on an even date. Two persons were born between the ones who like pink and blue. A was born before the one who likes green and two persons after the one who likes yellow. E doesn’t like yellow.

Which among the following pairs is correct?

To find the correct pair, let's analyze the given clues step-by-step to determine the birth month, birth date, and color preference for each of the six persons (A, B, C, D, E, and F).

The available months are April (30 days), July (31 days), and September (30 days).
The dates of birth are the 9th (odd date) and the 26th (even date) of these months.
This gives us six ordered slots from earliest to latest:
1. April 9th
2. April 26th
3. July 9th
4. July 26th
5. September 9th
6. September 26th

Step 1: Locate D and F
Clue: "D was born immediately before F on an odd date and in the month having even number of days."
The months having an even number of days (30 days) are April and September.
Since D is born on an odd date (9th) in one of these months, D must be born on either April 9th or September 9th.
Since D was born immediately before F, F must be born on the 26th of that same month.
Thus, the two possibilities are:
Case 1: D is born on April 9th, and F is born on April 26th.
Case 2: D is born on September 9th, and F is born on September 26th.

Step 2: Use the clue about F and Red
Clue: "Two persons were born between F and the person who likes red."
In Case 1 (F on April 26th, slot 2):
The person who likes Red must be born in slot 5 (September 9th) because there are exactly two persons (slots 3 and 4) between slot 2 and slot 5.
In Case 2 (F on September 26th, slot 6):
The person who likes Red must be born in slot 3 (July 9th) because there are exactly two persons (slots 4 and 5) between slot 6 and slot 3.

Step 3: Analyze E and C
Clue: "E was born immediately before C on an even date."
Since E is born on an even date (26th) and immediately before C, C must be born on the 9th of the following month. The possible pairs of (E, C) are:
- E in slot 2 (April 26th) and C in slot 3 (July 9th)
- E in slot 4 (July 26th) and C in slot 5 (September 9th)

Let's check if E can be in slot 2 (April 26th).
If E is in slot 2, then C is in slot 3. But in Case 1, F is in slot 2. So in Case 1, E cannot be in slot 2, which means E must be in slot 4 (July 26th) and C must be in slot 5 (September 9th).
In Case 2, F is in slot 6 (September 26th). If E is in slot 2 (April 26th) and C is in slot 3 (July 9th), then slot 5 is open. If E is in slot 4 (July 26th) and C is in slot 5 (September 9th), then slot 3 is open.

Step 4: Use the clue about Pink and C
Clue: "The one who likes pink was born two persons before C."
Being born "two persons before C" means there is exactly one person between the one who likes Pink and C.
If C is in slot 5 (September 9th), then the one who likes Pink must be in slot 3 (July 9th).
If C is in slot 3 (July 9th), then the one who likes Pink must be in slot 1 (April 9th).

Let's apply this to our cases:
Case 1:
- Slot 1 (April 9th): D
- Slot 2 (April 26th): F
- Slot 3 (July 9th): Likes Pink
- Slot 4 (July 26th): E
- Slot 5 (September 9th): C (Likes Red - from Step 2)
But this leads to a contradiction because C is in slot 5, meaning the person in slot 3 must like Pink. However, slot 5 is C, who likes Red, which is consistent. But wait, "Two persons were born between the ones who like pink and blue."
If Pink is in slot 3 (July 9th), then Blue must be in slot 6 (September 26th) since there must be two persons (slots 4 and 5) between Pink and Blue.
Let's verify the positions for Case 1:
- 1. April 9th: D
- 2. April 26th: F
- 3. July 9th: [Pink]
- 4. July 26th: E
- 5. September 9th: C [Red]
- 6. September 26th: [Blue]

Now let's check the clues about A and Yellow:
Clue: "A was born before the one who likes green and two persons after the one who likes yellow."
A being born "two persons after the one who likes yellow" means there is exactly one person between Yellow and A. This means:
Yellow is in slot $x$ and A is in slot $x+2$.
Also: "E doesn't like yellow."
Let's check the remaining empty slots for A and Yellow in Case 1.
The persons are D, F, E, C. The remaining two slots for persons are Slot 3 (July 9th) and Slot 6 (September 26th). So A and B must occupy these slots.
If A is in Slot 3 (July 9th), then Yellow must be in Slot 1 (April 9th) (which is D). E is in Slot 4, and E does not like yellow (which is consistent since D likes yellow).
If A is in Slot 3, then the person who likes Green must be after A. Since Slot 3 is Pink, Slot 5 is Red, Slot 6 is Blue, and Slot 1 is Yellow, the remaining colors are Green and White.
The remaining slots for colors are Slot 2 (F) and Slot 4 (E). Since A (Slot 3) is before Green, Green must be in Slot 4 (E) or Slot 6 (Blue - but Blue is already taken). Thus, Green must be in Slot 4 (E), and White must be in Slot 2 (F).
Let's verify this configuration:
- 1. April 9th: D (Yellow)
- 2. April 26th: F (White)
- 3. July 9th: A (Pink)
- 4. July 26th: E (Green)
- 5. September 9th: C (Red)
- 6. September 26th: B (Blue)

Let's double-check all clues against this configuration:
1. Six persons born in April, July, Sept on 9th and 26th: Yes.
2. Two persons between F (April 26th) and C (Sept 9th) who likes Red? Slots 3 and 4 are between them: Yes.
3. D was born immediately before F on an odd date in an even-day month: D on April 9th, F on April 26th: Yes.
4. The one who likes pink (A, July 9th) was born two persons before C (Sept 9th): Yes (one person, E, is between them).
5. E was born immediately before C on an even date: E on July 26th, C on Sept 9th: Yes.
6. Two persons between Pink (July 9th) and Blue (Sept 26th): Yes (slots 4 and 5 are between them).
7. A (July 9th) was born before the one who likes green (E, July 26th): Yes.
8. A (July 9th) was born two persons after the one who likes yellow (D, April 9th): Yes (F is between them).
9. E doesn't like yellow: E likes Green: Yes.

Thus, this configuration is completely consistent and correct. Looking at the options:
- B – Green, 26th September (Incorrect, B is Blue)
- C – Red, 26th July (Incorrect, C is 9th September)
- F – White, 26th April (Correct, F is White on 26th April)
- E – Green, 26th April (Incorrect, E is 26th July)