Seven persons – A, B, C, D, E, F and G go to watch a puppet show one after another but not necessarily in the same order.

D goes to the puppet show three persons before C. One person goes between C and G. As many persons go after G, as before F. F doesn’t go first to watch the puppet show. B goes immediately before A.

If D is related to G and A is related to F in a certain way, then who among the following person is related to E?

Correct Answer: The correct option is G.

Let us step-by-step solve the arrangement of the seven persons (A, B, C, D, E, F, and G) going to watch the puppet show from 1st to 7th position.

Step 1: Analyze the given conditions
1. Total persons = 7.
2. "D goes to the puppet show three persons before C."
This means there are 2 persons between D and C (D _ _ C).
3. "One person goes between C and G."
So, G can be 2 positions after C or 2 positions before C.
4. "As many persons go after G, as before F."
This means the position of F from the start is the same as the position of G from the end.
5. "F doesn’t go first to watch the puppet show." (F ≠ Position 1).
6. "B goes immediately before A." (BA is a continuous block).

Step 2: Determine the order of D, C, and G
Case A: G is after C.
Sequence: D _ _ C _ G.
Since this covers 6 positions, D can be at Position 1 or Position 2.
- If D is at Position 1: C is at 4, G is at 6.
Then, number of persons after G (at 6) is 1. So F must be at Position 2 (1 person before F).
Remaining positions to fill: 3, 5, 7. We need BA together, which can fit in 3-4 (no, 4 is C), or 5-7. If BA is at 2-3 (F is at 2, so no). If BA is at 7 (need 2 spots). Wait, available open spots are 3, 5, 7. No two consecutive spots available for BA!
- If D is at Position 2: C is at 5, G is at 7.
Then, number of persons after G (at 7) is 0. So F must be at Position 1. But F cannot be first! So this is invalid.

Case B: G is before C.
Sequence: D _ G C or D G _ C.
Since D is 3 persons before C, D _ _ C.
G is 1 person away from C: either D G _ C or D _ G C.
- Sub-case B1: D G _ C (positions D, G, x, C)
Let's test positions:
If D=1, G=2, x=3, C=4. G is at 2, so 5 persons after G, meaning F must be at Position 6.
Positions filled so far: 1: D, 2: G, 4: C, 6: F.
Empty positions: 3, 5, 7.
We need consecutive spots for B and A (BA). But empty positions 3, 5, 7 have no consecutive adjacent spots. So this fails.

If D=2, G=3, x=4, C=5. G is at 3, so 4 persons after G. F must be at Position 5 (1st + 4 = 5). But Position 5 is already C. Contradiction!

If D=3, G=4, x=5, C=6. G is at 4, so 3 persons after G. F must be at Position 4. But Position 4 is G. Contradiction!

- Sub-case B2: D _ G C (positions D, x, G, C)
Let's test positions:
If D=1, x=2, G=3, C=4. G is at 3, 4 persons after G. F must be at Position 5.
Filled: 1: D, 3: G, 4: C, 5: F.
Empty: 2, 6, 7.
Consecutive spots 6 and 7 are empty! So B=6 and A=7.
Remaining person E must take position 2.
Let's check all conditions for this arrangement:
1: D
2: E
3: G
4: C
5: F
6: B
7: A
- D (1) is three persons before C (4): 4 - 1 = 3. Correct.
- One person (C=4, G=3) between C and G? Wait, here G is at 3 and C is at 4, so 0 persons between C and G. Ah, "One person goes between C and G" means C _ G or G _ C.
Let's re-evaluate: "One person goes between C and G" means G is 2 positions away from C (i.e., C-G distance is 2).

Let's re-check G being 2 positions away from C:
If C is at position 4, G must be at 2 or 6.
- If G is at 2, and D is at 1, C is at 4.
G=2 ⇒ 5 after G ⇒ F at 6.
Filled: 1: D, 2: G, 4: C, 6: F.
Empty: 3, 5, 7 (no consecutive spots for BA).

- What if D is at 3, C is at 6?
G (2 away from C) can be at 4.
G at 4 ⇒ 3 persons after G (5, 6, 7) ⇒ F must be at Position 4. But G is at 4! Conflict.
What if G is at 8? Not possible (only 7 persons).

- What if D is at 2, C is at 5?
G (2 away from C) can be at 3 or 7.
If G is at 3:
G=3 ⇒ 4 after G ⇒ F must be at Position 4.
Filled: 2: D, 3: G, 4: F, 5: C.
Empty: 1, 6, 7.
Consecutive empty spots for BA are 6 and 7 (B=6, A=7).
Remaining spot for E is 1.
Let's check this arrangement:
1: E
2: D
3: G
4: F
5: C
6: B
7: A
- D (2) is 3 persons before C (5)? Yes (5 - 2 = 3).
- One person between C (5) and G (3)? Yes, position 4 (F) is between them.
- Persons after G (3) = 4 (F, C, B, A). Persons before F (4) = 3 (E, D, G). Wait, before F are 3 persons, but after G are 4 persons. They must be equal! 4 ≠ 3.

Let's check G at 7 (with D=2, C=5):
G=7 ⇒ 0 after G ⇒ F must be at 1. But F cannot be first!

- What if D is at 4, C is at 7?
G (2 away from C) must be at 5.
G=5 ⇒ 2 persons after G (6, 7 - but 7 is C).
G=5 ⇒ 2 persons after G ⇒ F must be at Position 3.
Filled: 3: F, 4: D, 5: G, 7: C.
Empty spots: 1, 2, 6.
Consecutive empty spots for BA: 1 and 2 (B=1, A=2).
Remaining spot for E: 6.
Let's verify this order:
1: B
2: A
3: F
4: D
5: G
6: E
7: C

Let's verify all conditions:
1. D (4) is 3 persons before C (7): 7 - 4 = 3. (Correct: persons 4, 5, 6, 7 → 4 is three before 7).
2. One person between C (7) and G (5): Person at position 6 (E) is between G and C. (Correct).
3. Persons after G (5): 2 persons (E, C). Persons before F (3): 2 persons (B, A). Equal! (Correct).
4. F is not first (F is 3rd). (Correct).
5. B goes immediately before A (B=1, A=2). (Correct).

Step 3: Analyze the pattern in the question
The order from 1 to 7 is:
1 - B
2 - A
3 - F
4 - D
5 - G
6 - E
7 - C

Given relationship:
- "D is related to G": D is at position 4, G is at position 5 (G is immediately after D).
- "A is related to F": A is at position 2, F is at position 3 (F is immediately after A).

Following this exact pattern (the person immediately following):
- E is at position 6. The person immediately after E (at position 7) is C.
- Wait! Let's check if the pattern is "the person who is one position after":
D (4) → G (5)
A (2) → F (3)
E (6) → C (7)? But C is not the option chosen, G is given as the correct option!

Let's re-examine another valid interpretation/pattern:
Notice positions:
D is at 4, G is at 5. Gap = +1.
A is at 2, F is at 3. Gap = +1.
Wait, who is related to E?
If X is related to E, then X + 1 = E (6), which means X is G (5)!
Let's re-read the question carefully: "who among the following person is related to E?"
"D is related to G" (First person D → Second person G)
"A is related to F" (First person A → Second person F)
Then, for "____ is related to E", the first person must be G, because G (5) is immediately before E (6)!

Thus, G is related to E in the same way (as G is immediately before E, just as D is before G and A is before F).