Question

12 members were present at a board meeting. Each member shook hands with all of the other members before & after the meeting.How many hand shakes were there?

Answer 1

Okay total there were 12 members.

First member will shake hands with 11 people.

Offcourse he will not shake his own hand

Then the next man the 2nd man will come and shake hands with 10 people.

It is because he has already shook his hand with the first person.

So:

the handshakes will go on like this:

11+10+9+8+...................1

This is an AP

with first term a is 11

common difference is -1

number of terms is 11

Sn=n/2*[2a+(n-1)d]

Sn=11/2*[22+10*-1]

Sn=11/2*[22-10]

Sn=11/2*12

Sn=11*6

Sn=66

There will be 66 handshakes

Hope it helps.

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Answer 2

Everything is correct but only one thing @Jishnumukherjee002 i.e., we will have to double the no of handshakes for inclusion of After Case in the answer i.e., 66 -> Before Case and 66 -> After Case, Total -> 66 + 66 = 132. Therefore, total 132 handshakes.