This problem requires calculating the number of students positioned between Hansa and Neeti in a single row, given their positions from opposite ends and the total number of students.
Calculating Hansa's Left Position
First, we determine Hansa's position from the left end. The total number of students is 97. Hansa is the 46th from the right.
- Position from left = (Total students) - (Position from right) + 1
- Hansa's position from left = $97 - 46 + 1$
- Hansa's position from left = $51 + 1 = 52^{\text{nd}}$
So, Hansa is 52nd from the left end.
Calculating People Between Hansa and Neeti
We know Neeti is 35th from the left and Hansa is 52nd from the left.
To find the number of people standing strictly between them, we subtract Neeti's position from Hansa's position and then subtract 1 (since we don't count Hansa or Neeti themselves).
- Number of people between = (Hansa's left position) - (Neeti's left position) - 1
- Number of people between = $52 - 35 - 1$
- Number of people between = $17 - 1 = 16$
Verification Using Total Students
Alternatively, consider the students to the left of Neeti and to the right of Hansa.
- Students to the left of Neeti = $35 - 1 = 34$
- Students to the right of Hansa = $46 - 1 = 45$
- Total students = (Students left of Neeti) + Neeti + (People between) + Hansa + (Students right of Hansa)
- $97 = 34 + 1 + (\text{People between}) + 1 + 45$
- $97 = 34 + 45 + 2 + (\text{People between})$
- $97 = 79 + 2 + (\text{People between})$
- $97 = 81 + (\text{People between})$
- People between = $97 - 81 = 16$
Both methods confirm that there are 16 people standing between Hansa and Neeti.
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