Question

A hotel bill for a number of people for overnight stay is Rs4800.
If there were 4 more people , the bill each person had to pay , would have reduced by 200 . Find the number of staying overnight .

Answer 1

Given :

The overstay bill amount in a hotel = Rs 4800

Total number of extra people = n = 4

The reduced amount for each people = Rs 200

To Find :

The number of people staying over night

Solution :

Let The number of people staying over night = x

According to condition

 $\dfrac{4800}{x}$-   $\dfrac{4800}{x+4}$  =  200

Solving this equation

 $\dfrac{4800 (x + 4) - 4800 x}{(x+4)x}$ = 200

Or,  4800 ( x + 4 ) - 4800 x = 200 × x × (x + 4)

Or,  4800 x + 19200 - 4800 x = 200 x² + 800 x

Or,  200 x² + 800 x - 19200 = 0

Or,   x² + 4 x - 96 = 0

Solving this quadratic equation

 x = $\dfrac{-4\pm \sqrt{(4)^{2}-4\times 1\times (-96)}}{2\times 1}$

   = $\dfrac{-4\pm \sqrt{400}}{2}$

   = $\dfrac{-4+20}{2}$            ,  $\dfrac{-4-20}{2}$

  = 8 , - 12

So, Number = x = 8

Hence, The number of people staying over night are 8   Answer

Answer 2

Answer:8

Step-by-step explanation:

Let the no of people staying over night = x

Bill paid by each = 4800/x

If people = x+4

Then bill paid by each = (4800/x)-200

(x+4) (4800/x-200) = (4800)

(x+4) (4800-200x) = 4800x

4800x + 19200 - 200x² - 800x = 4800x

(4800 cancels from both sides)

200x² + 800x - 19200 = 0

(simplifying equation, we get)

x² + 4x - 96 = 0

Solving this quadratic equation

x = (-4±√16+384)/2

= (-4±√400)/2

= (-4+20)/2 ; (-4-20)/2

x= 8 , - 12

So, Number = x = 8

Hence, The number of people staying over night are 8