#### Question

A hotel bill for a number of people for the 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.

#### Solution

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

Is there an error in this question or solution?

Solution A Hotel Bill for a Number of People for Overnight Stay is Rs 4800. If There Were 4 People More, the Bill Each Peson Had to Pay, Would Have Reduced by Rs 200. Find t Concept: Quadratic Equations.