There were 35 students in a hostel. If the number of students increase by 7, the expenses of the mess increase by Rs 42 per day while the average expenditure per head diminishes by Rs 1. Find the original expenditure of the mess?a)450b)420c)430d)410e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given Data:

- Initial number of students = 35
- Increase in number of students = 7
- Increase in expenses per day = Rs 42
- Decrease in average expenditure per head = Rs 1

Let's calculate:

Step 1: Calculate the initial total expenditure

Let the initial expenditure per head be Rs x.
Therefore, the initial total expenditure = 35x

Step 2: Calculate the new total expenditure

With the increase in number of students, the new total expenditure = (35 + 7)(x - 1)

Step 3: Calculate the increase in total expenditure

Increase in total expenditure = New total expenditure - Initial total expenditure
Increase in total expenditure = (42 * 42) - 35x

Step 4: Solve for the initial expenditure

Given that the increase in total expenditure = Rs 42
Therefore, 42 = 42 * 42 - 35x
Solving the above equation, we get x = Rs 420

Therefore, the original expenditure of the mess was Rs 420.

So, the correct answer is option B) 420.

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