Question

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.16
B.15
C.13
D.14

Answer 1

let total no. of people present in the party be x.
then,
x(x-1)/2=105
x=15

Answer 2

Answer:

Step-by-step explanation: handshake relates to two persons only

Let the total persons be n only

Each person handshakes another person.

Hence, no. Of handshakes = nC2 = 105

n(n-1) /1 x 2 = 105

n^2 - n = 210

n^2 -n - 210 = 0

(n-15) (n+14) = 0

n = 15 or n = -14

no. Of persons were present = 15 only.