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?
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?
Solution
Let Neetu be at position 7 from the front.
Let Mona be at position 6 from the back.
Let the total number of girls be .
Position of Neetu from the front
Position of Mona from the front
For Parul to stand between Neetu and Mona, there must be at least one position between them.
This requires:
Position of Neetu Position of Parul Position of Mona
For at least one position to exist between them:
Wait, this gives minimum as 13, but let's reconsider if Mona comes before Neetu.
If Mona's position (from back) places her before Neetu in the queue:
Position of Mona from front
For Mona to be before Neetu:
This gives
For minimum , we want Mona and Neetu as close as possible with Parul between them.
If :
- Neetu is at position 7 from front
- Mona is at position from front
- Parul can be at positions 4, 5, or 6 (between them)
This configuration satisfies all conditions.
Therefore, the minimum number of girls is .
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