Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is-

Question: Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is-

Solution:
⇒n(n - 1)/2 = 66
⇒n(n - 1) = 66 × 2
n² - n = 132
n² - n - 132 = 0
n² - 12n + 11n - 132 = 0
n(n - 12) + 11(n - 12) = 0
(n - 12)(n + 11) = 0
n = 12, - 11