Sum
A hotel bill for a number of people for the 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`'
`x^2 + 4x - 96 = 0`
`x^2 + 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 peple staying overnight is 8
Concept: Quadratic Equations
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