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?

Updated On: Jan 30, 2025
  • 14
  • 13
  • 15
  • 16
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The Correct Option is C

Solution and Explanation

The correct option is (C): 15
Explanation: The number of handshakes can be calculated using the formula n(n1)2=H\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:
  n(n1)2\frac{n(n-1)}{2} = 105     n(n1)=210\implies n(n-1) = 210
Testing n=15:
15(151)=15×14=21015(15-1) = 15 \times 14 = 210
Thus, there were 15 persons at the party.
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