Question

After a get-together every person present shakes the hand of every other person. If there were 105 hands shakes in all how many persons were present in the party?

• A. 14
• B. 13
• C. 15
• D. 16

Answer 1

Answer: (C)

15

Answer 2

The correct option is (C): 15
Explanation: The number of handshakes can be calculated using the formula $\frac{n(n-1)}{2} = H$, where n is the number of persons and H is the total number of handshakes. Here, H=105.
So, setting up the equation:
$\frac{n(n-1)}{2}$ = 105 $\implies n(n-1) = 210$
Testing n=15:
$15(15-1) = 15 \times 14 = 210$
Thus, there were 15 persons at the party.