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.

• A. $5$
• B. $8$
• C. $6$
• D. $7$

Answer 1

The correct option is B $8$

Let the number of people staying overnight be $x$.

For x people, the hotel bill =$Rs.4800$

For $1$ person, the hotel bill = $\frac{4800}{x}$

When $4$ people were more, the hotel bill = $\frac{4800}{x+4}$

The bill paid by each person is reduced by $Rs.200$.

Therefore, $\frac{4800}{x}-\frac{4800}{x+4}=200$

$\frac{4800(x+4)-4800x}{x(x+4)}=200$

$4800x+19200-4800x=x^2+4x=\frac{19200}{200}=96$

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

Using $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to find the roots of the equation

$\Rightarrow x=\frac{-4\pm \sqrt{(4{)}^2-4\times 1\times (-96)}}{2\times 1}$

$\Rightarrow x=\frac{-4\pm \sqrt{400}}{2}$

$\Rightarrow x=\frac{-4\pm 20}{2}$

$x=8$, $x=-12$

$x$ cannot be negative as it denotes the number of people.

Number of people staying overnight = $8$