# A group of friends goes for dinner and gets bill of Rs 2400. Two of them says that they have forgotten their purse so remaining make an extra contribution of Rs 100 to pay up the bill. Tell the no. of person in that group ?

A group of friends goes for dinner and gets bill of Rs 2400. Two of them says that they have forgotten their purse so remaining make an extra contribution of Rs 100 to pay up the bill. Tell the no. of person in that group ?

Let 'x' be the number of perons in the group and let 'y' be amount per head which they have to pay.
Then xy = 2400.
or y = 2400/x
Since two friends have forget the purse, x-2 persons should share the total amount(2400).

If they share, they have to make an extra contribution of Rs 100 to pay up the bill That is x-2 persons should pay y+100 each
or (x-2)(y+100) = 2400
or y+100 = 2400/(x-2)
or y = 2400/(x-2) - 100

Therefore we have got two equations namely,
y= 2400/x and
y = 2400/(x-2) - 100

Comparing these two, we get
2400/x = 2400/(x-2) - 100

Solving this we get
x^2 - 2x -48 = 0
or (x-8) (x+6) = 0
or x = 8 or x = -6

Since 'x' denote the number of persons, it should be positive.
So, x = 8.