Question

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Answer 1

The correct answer is 10 .
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Here is the ans :-
If there are n people at the party, then each person will shake hands
with n-1 other people. So with n people each making (n-1) handshakes,
it appears at first sight that there are n(n-1) handshakes.

However, each handshake will have been counted twice, i.e. A shakes his hand with B then at the same time
B also shakes his hand with A, so we must divide by 2.

Total number of handshakes = n(n-1)/2

Now we are given that there were 45 handshakes in all, so we must
solve the equation:

n(n-1)/2 = 45

n(n-1) = 90

n^2 - n - 90 = 0

(n-10)(n+9) = 0 From this n = 10 or -9

Clearly the -9 has no meaning in this question, so we conclude that
n = 10

Number at the party = 10