Question

The hotel bill for a number of people for overnight stay is ₹4800. If there were 4 more the bill of each person had to pay would have reduced by ₹200. Find the number of people staying over night

Answer 1

8

Explanation:

Given hotel bill = ₹4800

Let initially, number of people =
`x`

Initial Bill of each person = Hotel bill divided by number of people =
`(4800)/(x)`

4 people are added to the hotel stay.

i.e. new number of people =
`x+4`

New bill becomes ₹200 less for each person.

New bill for each person =
`(4800)/(x)` - 200

Hotel bill remains the same i.e. ₹4800 = New bill for each person multiplied by new number of people.

`4800 = ((4800)/(x)-200) (x+4)\\\Rightarrow 4800 = (4800)/(x)* x -200* x + (4800)/(x)* 4 - 200* 4\\\Rightarrow 4800 = 4800 -200 x + (4800)/(x)* 4 - 800 \\\Rightarrow 800 = -200x+(19200)/(x)\\\Rightarrow 4 = -x+(96)/(x)\\\Rightarrow x^2+4x-96=0 \\\Rightarrow x^2+12x-8x-96=0\\\Rightarrow x(x+12)-8(x+12)=0\\\Rightarrow \bold{x = 8}, x= -12\ not\ possible`