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?
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: Sep 25, 2024
- 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 \(\frac{n(n-1)}{2} = H\), 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.
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.
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