Answer 1

Let the number of people staying overnight be x

Total hotel bill = Rs 4800

Hotel bill for each person = Rs `4800/"x"`

From the given information

`4800/x - 4800/(x + 4) = 200`

`(4800x + 4800 xx 4 - 4800x)/(x(x + 4))= 200`

`96/(x^2 + 4x) = 1`'

`x^2 + 4x - 96 = 0`

`x^2 + 12x - 8x - 96 = 0`

x(x + 12) - 8(x + 12) =0

(x - 8)(x + 12) = 0

x = 8, -12

Since the number of people cannot be negative So x = 8

Thus the number of peple staying overnight is 8