Question

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

• A. 10
• B. 12
• C. 8
• D. None of these

Answer 1

The correct option is C

8

Let the number of persons who stayed overnight in the hotel be x.

The amount of bill each person had to pay = $Rs\frac{4800}{x}$

The amount of bill each persons had to pay when there were 4 more persons = $Rs\frac{4800}{x+4}$ It is given that the amount of bill each person had to pay would have been reduced by Rs 200 if there were 4 more persons.$\begin{array}{cccccc}\therefore & \frac{4800}{x}-\frac{4800}{x+4}=200\Rightarrow & x^2+4x-96=0& Onsolving\Rightarrow & x=8orx=-12But,x=-12isnotpossible.\therefore & x=8\end{array}$ Hence, there were 8 people in the hotel.