Question

In a hostel it costs 1800 rupees to keep 50 children for 8 weeks. For what length of time did the cost of keeping 90 children amount to Rs.21060.

Answer 1

let the cost of 1 day = Rs x
cost for 56 days=56x
A.T.Q
56x+50y=1800
x+90y=21060
x=21060-90y
56(21060-90y)+50y=1800
1179360-5040y+50y=1800
then calculate on your and put this value of y in eq x
the value of x will be your answer

Answer 2

The hostel cost for 50 children for 8 weeks is Rs.1800

The hostel cost for 1 child for 8 weeks is 1800/50

The hostel cost for 1 child for 1 week is 1800/(50*8)

Thus, hostel cost for 90 children for 1 week is 1800*90/(50*8)

The cost of keeping 90 children for x number of weeks amounts to Rs.21060.

Thus, 1800*90*x/(50*8) = 21060,
=> x = 21060*50*8/(1800*90)
=> x = 842400/16200
=> x = 52
Thus, the number of weeks is 52 weeks (ans).


Hope it helps you.
Thank you.