Question 106

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?

Solution

Total number of handshakes = 105, let number of persons be $$x$$

=> Number of handshakes =$$\left(x-1\right)+\left(x-2\right)+...+1=\frac{x(x-1)}{2}=105$$

=> $$x^2-x-210=0$$

=> $$(x-15)(x+14)=0$$

=> $$x=15,-14$$

$$\because -14$$ is not possible, hence number of persons = 15

=> Ans - (C)

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