In a hostel there are 30 students and if the number of students increased by 5 then the expense is increased by 40 per day. But the average expenditure diminishes by 3. Find the original expenditure.a)810b)870c)910d)950e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

X - cost/person
30x+40 = 35x -3(35)
New cost of mess = New cost students (total)
Old cost of mess+added cost = Old of students - reduced average

Hence 5x=145 x=29
30*29=890

Answer

Answer – 2.870 Explanation : Let average expenditure be P. (30*P + 40)/35 = P-3
P = 29. So expenditure = 29*30 = 870

Answer

Given:
Number of students in the hostel = 30
Increase in number of students = 5
Increase in expense = 40

To find:
Original expenditure

Let the original expenditure be x.

Calculations:

When the number of students increases from 30 to 35, the total expenditure increases by 40.
So, we can write:

35x - 30x = 40

Simplifying the above equation, we get:

5x = 40

x = 8

So, the original expenditure was 8 units.

Now, it is given that when the number of students increases by 5, the average expenditure diminishes by 3.

Let the new expenditure be y.

Then, we can write:

y = (35x)/(30+5)

y = (35x)/35

y = x

So, the new expenditure is same as the original expenditure which is 8 units.

Therefore, the correct option is (B) 870.

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