There are 35 students in a hostel. If the number of students is increased by 7, the expenditure on food increases by Rs. 42 per day, while the average expenditure per student per day is reduced by Rs. 1. What was the initial total expenditure on food per day for the hostel?

Introduction / Context:
This is a classic average and total expenditure problem often asked in banking and management entrance tests. A hostel increases its number of students and sees that the total food expenditure rises, but the average expenditure per student falls. You must translate this situation into equations and determine the original total expenditure on food per day.

Given Data / Assumptions:
- Initial number of students in the hostel = 35.
- When 7 more students join, the total number becomes 42.
- Total food expenditure increases by Rs. 42 per day after the increase in strength.
- Average expenditure per student per day is reduced by Rs. 1 after the increase.
- We must find the initial total food expenditure per day in rupees.

Concept / Approach:
The average expenditure per student is defined as total expenditure divided by number of students. If we let the initial average be x rupees per student per day, then the initial total is 35x. After the increase, the new average is (x - 1) and the new total is 42(x - 1). The increase in total expenditure is equal to the difference between these totals, and it is given as Rs. 42. Setting up an equation from this information allows us to solve for x and then find the original total expenditure.

Step-by-Step Solution:
Step 1: Let the initial average expenditure per student per day be x rupees.Step 2: Initial total expenditure per day = 35 * x.Step 3: After 7 more students join, total students = 42 and the new average becomes x - 1.Step 4: New total expenditure per day = 42 * (x - 1) = 42x - 42.Step 5: Given that the total expenditure increases by Rs. 42, we have 42x - 42 - 35x = 42.Step 6: Simplify the left side: 7x - 42 = 42.Step 7: Add 42 to both sides: 7x = 84, so x = 84 / 7 = 12.Step 8: Initial total expenditure per day = 35 * 12 = Rs. 420.

Verification / Alternative check:
If the initial average is Rs. 12, initial total expenditure is 35 * 12 = Rs. 420. After 7 students join, total students = 42 and new average = 11 rupees per student per day. The new total expenditure is 42 * 11 = Rs. 462. The increase in total expenditure is 462 - 420 = Rs. 42, and the change in average is 12 - 11 = Rs. 1, both of which match the conditions in the problem. This confirms that the answer is correct.

Why Other Options Are Wrong:
If the initial total were Rs. 432, 442 or 400, the corresponding averages per student would not lead to a new total that is exactly Rs. 42 higher while also reducing the average by Rs. 1. Substituting these totals into the scenario leads to inconsistent averages or incorrect increases in total expenditure. Only Rs. 420 satisfies all given conditions.

Common Pitfalls:
Many students confuse the change in average with the change in total and try to subtract 1 directly from the total instead of from the per student value. Others forget that the number of students changes from 35 to 42 and therefore use the wrong multiplier when computing new expenditure. Always start with a variable for the average, compute both totals, and then use the given increase to construct a correct equation.

Final Answer:
The initial total expenditure on food per day was Rs. 420.