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?

16

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15

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13

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14

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Solution

The correct option is A $15$
Total number of handshakes $= 105$
Let number of person be $= x$
Number of handshakes
$= \frac{x (x - 1)}{2} = 105 \Rightarrow x (x - 1) = 210 x = 15$
Hence the correct answer is $15$

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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?

The correct option is A 15Total number of handshakes =105Let number of person be =xNumber of handshakes =x(x−1)2=105⇒x(x−1)=210x=15Hence the correct answer is 15

The correct option is A $15$
Total number of handshakes $= 105$
Let number of person be $= x$
Number of handshakes
$= \frac{x (x - 1)}{2} = 105 \Rightarrow x (x - 1) = 210 x = 15$
Hence the correct answer is $15$