Question

A group of students went out for lunch

after their examination. They were to
share the expenses equally. The total bill
was R200. Ten of the students did not
have any money, so each of the others
had to pay an extra R1. Determine the
number of students in the group.

Answer 1

number sof student of the group is 50

Explanation:

let the number students be x

total bill is Rs 200

each student will pay =200/x

now 10 students do not have the money

so x - 10 students will pay the bill of Rs 200

according to the problem

`(200)/(x-10)` =
`(200)/(x)` + 1

or,
`(200)/(x-10)` -
`(200)/(x)` = 1

or, 200 (
`(1)/(x-10)` -
`(1)/(x)`) = 1

or, 200(
`(x-x+10)/(x(x-10))`) = 1

or, 200 X 10 = x(x-10)

or,
`x^(2)` - 10x - 2000 = 0

or,
`x^(2)` - 50x +40x - 2000 =0( using middle term factor)

or, (x - 50) (x+40) = 0

x = 50 ( x = -40 for number of students it is not possible)