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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.
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`
x2 + 4x – 96 = 0
x2 + 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 people staying overnight is 8.
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