There were 45 students in a hostel, if the numbers of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What

 There were 45 students in a hostel, if the numbers of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What

A). Rs. 555

B). Rs. 585

C). Rs. 685

D). Rs. 655

Let the original average expenditure per student per day be $ x $.
Then, the total expenditure per day for 45 students is:

$ 45x $

After 7 more students join, the number of students becomes $ 45 + 7 = 52 $.
The total expenditure increases by Rs. 39, so the new total expenditure per day is:

$ 45x + 39 $

Since the average expenditure per student decreases by Re. 1, the new average expenditure per student is $ x - 1 $.
Thus, we set up the equation:

$ \frac{45x + 39}{52} = x - 1 $

Solving for $ x $:
Multiplying both sides by 52:

$ 45x + 39 = 52(x - 1) $

Expanding:

$ 45x + 39 = 52x - 52 $

Rearranging:

$ 45x - 52x = -52 - 39 $

$ -7x = -91 $

$ x = 13 $

Now, calculating the original total mess expenditure per day:

$ 45x = 45 \times 13 = 585 $

Thus, the correct answer is:

$ \boxed{585} $

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