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In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party?
- a)15
- b)14
- c)16
- d)17
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a get-together party, every person present shakes the hand of every...
Problem:
In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party?
Solution:
Let there be 'n' persons present at the party.
Each person shakes hands with every other person, so the total number of handshakes will be:
nC2 = n(n-1)/2
Given that the total number of handshakes is 90, so we have:
n(n-1)/2 = 90
n(n-1) = 180
n^2 - n - 180 = 0
Solving this quadratic equation, we get:
n = 14 or n = -13
Since the number of persons cannot be negative, so the number of persons present at the party is 14.
Answer: Option B (14)
In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party?
Solution:
Let there be 'n' persons present at the party.
Each person shakes hands with every other person, so the total number of handshakes will be:
nC2 = n(n-1)/2
Given that the total number of handshakes is 90, so we have:
n(n-1)/2 = 90
n(n-1) = 180
n^2 - n - 180 = 0
Solving this quadratic equation, we get:
n = 14 or n = -13
Since the number of persons cannot be negative, so the number of persons present at the party is 14.
Answer: Option B (14)
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Community Answer
In a get-together party, every person present shakes the hand of every...
Let the total number of persons present at the party be m, Then, [{x *(x−1)}/2] = 90.
x = 14.
x = 14.
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