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.

• Lets get there without the 8...
  
  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
  100 Rs 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' denotes the number of persons, it should be positive.
  So, x = 8.
• 10 years agoHelpfull: Yes(13) No(0)
• Total 8 friends
  Actual share=300
  But 2 didn't give their amount so 600 would be required to share..
  other 6 would give 100 each to pay bill
• 12 years agoHelpfull: Yes(8) No(19)
• please explain how it comes to (x-8)(x+6) from the equation ?
• 8 years agoHelpfull: Yes(0) No(1)
• Let s consider there are 8 friends in that group then
  8 members need to contribute 2400 so per head it is 300
  as per the problem two persons dont have money so the rest 6 members paid 100 extra each
  so the equation is
  6*300(per head)+6*100(extra)= 2400
  so the number of people in that group is "8".
• 3 years agoHelpfull: Yes(0) No(0)