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A Hotel Bill for a Number of People for Overnight Stay is Rs 4800. If There Were 4 People More, the Bill Each Peson Had to Pay, Would Have Reduced by Rs 200. Find t - ICSE Class 10 - Mathematics

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Question

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.

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

  Is there an error in this question or solution?

APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 3
Solution A Hotel Bill for a Number of People for Overnight Stay is Rs 4800. If There Were 4 People More, the Bill Each Peson Had to Pay, Would Have Reduced by Rs 200. Find t Concept: Quadratic Equations.
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