After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?

A.

14

B.

13

C.

15

D.

16

• Total no. of Handshakes : nC2
  where n is the no. of person, and 2 person can handshake at one time.
  so nC2= 105
  n(n-2)/2=105
  n^2-n-210=0
  this means: n=-14 and n=15
  taking positive values: Ans = 15.
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