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

After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party? Correct Answer 15

Let total number of persons present in the party be x,Then,$$\eqalign{ & \frac{{x \times \left( {x - 1} \right)}}{2} = 105 \cr & x = 15 \cr} $$

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