Question

in a hostal of 50 students, the monthly miscellaneous expenses were increased by ₹152, when the no. of students increased by 14.
the average monthly expenses were therefore, reduced by ₹2 per head. find the original rate of miscellaneous expenses per student, per month.​

Answer 1

Step-by-step explanation:

Let the food expense per day be x and the constant expense be y

Given, 20x+y=1700 --- (1)

And 24x+y=1900 -- (2)

Subtracting equation (1) from (2), we get

4x=200⇒x=50

Substituting x=50 in the equation (1), we get 20(50)+y=1700⇒y=700

Hence, food expenses per day = Rs. 50 and fixed charge = Rs. 700

Answer 2

Step-by-step explanation:

Average monthly expenses= x

Total expenses= 50(x)

when increase in students by 14

50+14= 64 students

Now total expenses for 64 students= 50(x)+152

average monthly expenses reduced by 2 per head.

Av= x-2 Average exp= total expenses/no of students

x-2=50(x)+152/64

64(x-2)= 50x + 152

64x-128= 50x+152

64x-50x= 152+128

14x= 280

x= 280/14

x= 20

Therefore Average monthly expenses= x= 20

Total expenses = 50(x) = 50×20= 1000