Question

A hotel bill for a number of people for overnight stay is Rs. 4800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs. 200. Find the number of people staying overnight.

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`

x² + 4x – 96 = 0

x² + 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 people staying overnight is 8.