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.

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Solution

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 = $R s \frac{4800}{x}$

The amount of bill each persons had to pay when there were 4 more persons = $R s \frac{4800}{x + 4}$ 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. $\begin{matrix} ∴ & \frac{4800}{x} - \frac{4800}{x + 4} = 200 \Rightarrow & x^{2} + 4 x - 96 = 0 & O n s o l v i n g \Rightarrow & x = 8 o r x = - 12 B u t, x = - 12 i s n o t p o s s i b l e . ∴ & x = 8 \end{matrix}$ Hence, there were 8 people in the hotel.

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