A hostel has 35 students. When 7 more students join (making 42), the daily mess expense increases by Rs 42, yet the average expense per head decreases by Re 1. What was the original total daily mess expense?

Introduction:
This is a classic average cost problem. Increasing the headcount changes both the total and per-head costs. We set up two equations: one for the new total expense and another linking new per-head cost to the old per-head cost minus Re 1, then solve for the original total expense.

Given Data / Assumptions:

• Original students = 35; new students = 42
• Increase in total expense = Rs 42
• Decrease in per-head expense = Re 1

Concept / Approach:
Let original total expense be E. Then original per-head = E / 35. New total = E + 42, so new per-head = (E + 42) / 42. Given (E + 42) / 42 = (E / 35) − 1. Solve for E.

Step-by-Step Solution:

Verification / Alternative check:
Original per-head = 420 / 35 = 12. New total = 462; new per-head = 462 / 42 = 11, exactly Re 1 less.

Why Other Options Are Wrong:
432, 442, 40, and 410 fail the per-head check when substituted back into the relationships.

Common Pitfalls:
Subtracting Rs 42 from per-head instead of adjusting totals; mixing up “increase” and “decrease”.

Final Answer:
Rs. 420