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In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
A). Rs.5000
B). Rs.4600
C). Rs.5400
D). Rs.2300
This Question has 1 answers.
$ E_1 = 100A $
When 20 more students join, the new number of students is
$ N' = 120 $
The new average expenditure per student is
$ A' = A - 5 $
The new total expenditure is
$ E_2 = 120(A - 5) $
Given that the total expenditure increased by Rs. 400,
$ E_2 = E_1 + 400 $
Substituting the values,
$ 120(A - 5) = 100A + 400 $
Expanding the equation,
$ 120A - 600 = 100A + 400 $
Solving for A,
$ 120A - 100A = 600 + 400 $
$ 20A = 1000 $
$ A = 50 $
Now, calculating the new total expenditure,
$ E_2 = 120(A - 5) $
$ E_2 = 120(50 - 5) $
$ E_2 = 120 \times 45 $
$ E_2 = 5400 $
So, the total expenditure of the hostel now is Rs. 5400.
When 20 more students join, the new number of students is
$ N' = 120 $
The new average expenditure per student is
$ A' = A - 5 $
The new total expenditure is
$ E_2 = 120(A - 5) $
Given that the total expenditure increased by Rs. 400,
$ E_2 = E_1 + 400 $
Substituting the values,
$ 120(A - 5) = 100A + 400 $
Expanding the equation,
$ 120A - 600 = 100A + 400 $
Solving for A,
$ 120A - 100A = 600 + 400 $
$ 20A = 1000 $
$ A = 50 $
Now, calculating the new total expenditure,
$ E_2 = 120(A - 5) $
$ E_2 = 120(50 - 5) $
$ E_2 = 120 \times 45 $
$ E_2 = 5400 $
So, the total expenditure of the hostel now is Rs. 5400.
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