Question

In a meeting each person present shook hands with every other person . If in total there were 66 shake hands , find how many persons were present in the meeting?

Answer 1

let total came to meeting be X,then

1st member gives X-1 shake hands
similarly 2nd gives X-2 s.h
3rd gives X-3 s.h
................................
................................
(X-1)th person gives 1s.h
Xth person gives 0s.h


total number of shake hands=1+2+.....+(X-2)+(X-1)
= (X-1)(X-1+1)/2

66 =X(X-1)/2
BY SOLVING
X=12.



above used formula :1+2+3+......+N=N(N+1)/2