Calculation with number of Shake hands

PSC and other competitive exams always contains questions with shake hands. Lets see how can we solve the questions with shake hands

Type 1: Find Shake hands if number of people is given

Total Number of shake hands exchanged if n people shake hands each other = (n²-n)/2 = (n(n-1))/2

Q1: How many shake hands were exchanged in a meeting with 20 people?

(n²-n)/2
=(20²-20)/2
=(400-20)/2
=190

Type 2: Find Number of people if Shake hands is given

Number of people  = The Biggest among the consecutive factor of double the number of Shake hands

Q2: In a meeting 45 shake hands were exchanged. Then how many people attended the meeting?

Total number of shake hands exchanged = 45
Multiply the total number of shake hands by 2 i.e. 45 x 2 = 90
Consecutive factors of 90 = 10 and 9 (10 x 9 = 90)
Bigger among them is 10
So the answer is 10

Q3: In a meeting 36 hand shakes were exchanged. Then how many people attended the meeting?

Total number of shake hands exchanged = 36
Multiply the total number of shake hands by 2 i.e.  36 x 2 = 72
Consecutive factors of 90 = 8 and 9 (i.e. 8 x 9 = 72)
Bigger among them is 9
So the answer is 9

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