Each student in Class IX contributes an amount equal to the square of the total number of students. If the total collection is Rs 29,791, find the total number of students.

Introduction:
The original stem is ambiguous. Applying the recovery-first policy, interpret it so the total becomes a perfect cube: if there are n students and each pays n^2 rupees, then the total T = n * n^2 = n^3. This matches the provided total of 29,791 (which is 31^3).

Given Data / Assumptions:

• Total amount collected T = Rs 29,791
• Recovered assumption: contribution per student = n^2 rupees
• Total students = n

Concept / Approach:
Use T = n^3. Take the cube root of 29,791 to find n.

Step-by-Step Solution:
T = n^3n = cube_root(29,791) = 31Check: 31^3 = 29,791

Verification / Alternative check:
If one instead assumed each pays n rupees, then T = n^2, but 29,791 is not a perfect square; thus the recovered assumption (n^2 per student) is consistent with the data.

Why Other Options Are Wrong:
30, 33, 40 do not satisfy n^3 = 29,791.

Common Pitfalls:
Misreading the contribution rule and treating 29,791 as a square instead of a cube; failing to apply the recovery-first interpretation to align with given total.

Final Answer:
31