Question

A hotel bill for a number of people for overnight stay is Rs. 4,800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs. 200. Find the number fo people staying overnight.

Answer 1

let the number of people staying be x
so
each person has to pay = $\frac{4800}{x}$
if 4 more were staying each person has to pay =$\frac{4800}{x+4}$ \

as per the problem
$\frac{4800}{x}-\frac{4800}{x+4}=200$
$\frac{4800(x+4-x)}{x^2+4x}=200$
$24\left(4\right)=x^2+4x$
​​ $x^2+4x-96=0$

D = 16 + 384 = 400
$\sqrt{D}=20$
x = $\frac{-b+\sqrt{D}}{2a},\frac{-b-\sqrt{D}}{2a}$

=$\frac{-4+20}{2},\frac{-4-20}{2}$
Now $\frac{-4-20}{2}$ is rejected because number of people cannot be negative

So taking $\frac{-4+20}{2}$ we have
= $\frac{16}{2}=8$
$\therefore$ there were 8 people orginally staying overnight