In a queue of girls, Neetu is seventh from the front. Mona is sixth from the back. Parul is standing in between the two. What could be the minimum number of girls standing in the queue?

8

The correct answer is Option (2) → 8

To find the minimum number of girls in the queue, we need to consider an overlapping scenario rather than a simple linear addition.

1. Understanding the Positions

• Neetu: 7th from the front.
• Mona: 6th from the back.
• Parul: Standing exactly in between Neetu and Mona.

2. Calculating the Minimum (Overlapping Case)

In a minimum number scenario, we try to place the person from the back (Mona) closer to the front than the person from the front (Neetu).

Let's test the smallest possible numbers based on the constraints:

• If Neetu is 7th from the front, there must be at least 7 girls.
• If we assume there are 8 girls in total:
• Neetu (7th from front): She is at position 7.
• Mona (6th from back): In a queue of 8, the 6th from the back is position $(8 - 6 + 1) = 3$.
• Check for Parul: Between position 3 (Mona) and position 7 (Neetu), the positions are 4, 5, and 6. The middle position is 5.
• Since there is an exact middle position (position 5), Parul can stand there.

3. Verification

• Total Girls: 8
• Neetu: Position 7 (7th from front) — Valid
• Mona: Position 3 (1, 2, 3, 4, 5, 6, 7, 8 $\rightarrow$ 3 is 6th from the back) — Valid
• Parul: Position 5 (Exactly between 3 and 7) — Valid

If we tried 7 girls, Mona would be at position 2, and the gap between 2 and 7 would contain positions 3, 4, 5, 6 (no single middle person for Parul). Thus, 8 is the absolute minimum.

Final Answer: The minimum number of girls standing in the queue is 8.