Question

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

Answer 1

Let the number of people = x
Amount of bill = Rs. 4800
Then bill for each person = Rs. `(4800)/x`
In second case,
the number of people = x + 4

then bill of each person = `(4800)/(x + 4)`
According to the condition,

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

⇒ `4800(1/x - 1/(x + 4))` = 200

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

⇒ `(4800 xx 4)/(x(x + 4)` = 200

⇒ 19200 = 200x² + 800x
⇒ 200x² + 800x - 19200 = 0
⇒ x² + 4x - 96 = 0  ...(Dividing by 200)
⇒ x² + 12x - 8x - 96 = 0
⇒ x(x + 12) -8(x + 12) = 0
⇒ (x + 12)(x + 8) = 0
Either x + 12 = 0,
then x = -12,
but it is not possible as it is in negative
or
x - 8 = 0,
then x = 8
∴ No. of people = 8.