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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.
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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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