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

How many persons go after B?

The correct option is Six.

Step-by-Step Explanation:

Let us arrange the seven persons (A, B, C, D, E, F, G) in order from position 1 (first to go) to position 7 (last to go).

Step 1: Analyze the given conditions:

1. Total number of persons = 7 (Positions 1 to 7).

2. D goes three persons before C. This means there are 2 persons between D and C (D _ _ C).

3. One person goes between C and G.

4. As many persons go after G, as before F.

5. F doesn't go first to watch the puppet show (F ≠ Position 1).

6. B goes immediately before A (BA is a combined unit).

Step 2: Determine positions for D, C, and G:

Since D _ _ C takes up 4 consecutive positions, let's explore possible positions for D and C:

Case 1: D is at 1, C is at 4.

Case 2: D is at 2, C is at 5.

Case 3: D is at 3, C is at 6.

Case 4: D is at 4, C is at 7.

Now consider G (One person goes between C and G):

In Case 1 (C at 4): G could be at 2 or 6.

- If G is at 2: Persons after G = 5. So persons before F must be 5 ⇒ F is at 6. Positions filled: D(1), G(2), C(4), F(6). Remaining positions: 3, 5, 7. We need adjacent spots for BA. Positions 3 and 5 are not adjacent, nor 5 and 7. Thus BA cannot fit.

- If G is at 6: Persons after G = 1. So persons before F must be 1 ⇒ F is at 2. Positions filled: D(1), F(2), C(4), G(6). Remaining empty positions: 3, 5, 7. No two adjacent empty positions for BA. Thus invalid.

In Case 2 (C at 5): G could be at 3 or 7.

- If G is at 3: Persons after G = 4. So persons before F must be 4 ⇒ F is at 5, but position 5 is occupied by C. Invalid.

- If G is at 7: Persons after G = 0. So persons before F must be 0 ⇒ F is at 1. Positions filled: F(1), D(2), C(5), G(7). Empty positions: 3, 4, 6. Here, positions 3 and 4 are adjacent! So B can be at 3 and A can be at 4. The remaining position 6 goes to E.

Let's check this arrangement from Case 2 (G at 7):

Position 1: F

Position 2: B (Wait, if B is at 1 and A at 2, let's check: B goes immediately before A, so B=1, A=2? No, let's verify positions 3 and 4 for B and A, or position 1 for B?)

Let's place B and A in the open slots for Case 2 (F at 1, D at 2, C at 5, G at 7):

Empty spots are 3, 4, 6.

If B = 3 and A = 4, then E = 6.

Order: 1-F, 2-D, 3-B, 4-A, 5-C, 6-E, 7-G.

Let's check if F is first: Condition says "F doesn’t go first to watch the puppet show". Since F is at position 1 here, this case is invalid!

Now let's check Case 3 (D at 3, C at 6):

G can be at 4.

- If G is at 4: Persons after G = 3. Persons before F must be 3 ⇒ F is at 4, but 4 is G. Invalid.

What if G is at 7? Wait, distance between 6 and 7 is 0, but one person goes between C and G, so G cannot be at 7 or 5 if C is at 6. G must be at 4.

Let's re-evaluate: What if B goes first (Position 1)?

If B is at 1, then A is at 2.

Then 6 persons go after B (Positions 2, 3, 4, 5, 6, 7).

Let's complete the order with B = 1, A = 2:

If B = 1, A = 2, then D must be at 3, C at 6 (3 persons before C is D, so 3, 4, 5, 6 -> D is at 3, C is at 6).

One person goes between C and G ⇒ G is at 4.

Persons after G = 3 (positions 5, 6, 7). Persons before F = 3 ⇒ F is at position 4? But G is at 4. Wait, let's check G at 4:

If G is at 4, persons after G are 5, 6, 7 (3 persons). Persons before F should be 3 ⇒ F must be at 4, which overlaps. But wait! What if D is at 4, C is at 7?

Then G is at 5 (one person between C at 7 and G at 5).

Persons after G(5) = 2 (positions 6, 7). So persons before F = 2 ⇒ F is at 3.

Positions filled: F(3), D(4), G(5), C(7).

Empty positions: 1, 2, 6.

Since B goes immediately before A, B = 1 and A = 2!

The remaining position 6 is occupied by E.

Step 3: Verify the full arrangement:

Position 1: B

Position 2: A

Position 3: F

Position 4: D

Position 5: G

Position 6: E

Position 7: C

Let's check all conditions:

1. D(4) goes 3 persons before C(7) [4 is 3 before 7: 4, 5, 6, 7] - Correct.

2. One person between C(7) and G(5) (which is E at 6) - Correct.

3. Persons after G(5) = 2 (E, C). Persons before F(3) = 2 (B, A) - Correct.

4. F doesn't go first (F is 3rd) - Correct.

5. B goes immediately before A (B is 1st, A is 2nd) - Correct.

Conclusion:

B goes at position 1. Since there are 7 persons in total, the number of persons who go after B is 7 - 1 = 6.

Therefore, Six persons go after B.