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Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14?
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Every two persons shakes hands with each other in a party and the tota...
Solution:
Let's assume there are n guests in the party.
To find the number of handshakes, we can use the formula n(n-1)/2. (Every guest shakes hands with n-1 other guests, but we divide by 2 because each handshake is counted twice).
According to the problem, the total number of handshakes is 66.
Therefore, we can set up the equation:
n(n-1)/2 = 66
Simplifying this equation gives:
n(n-1) = 132
Expanding the left side of the equation gives:
n^2 - n = 132
Bringing all the terms to one side of the equation gives:
n^2 - n - 132 = 0
Now we can use the quadratic formula to solve for n:
n = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -1, and c = -132.
Plugging these values into the formula gives:
n = (1 ± sqrt(1 - 4(1)(-132))) / 2(1)
Simplifying this equation gives:
n = (1 ± sqrt(529)) / 2
Since we are looking for a positive integer value of n, we can discard the negative solution and simplify further:
n = (1 + 23) / 2 or n = (1 - 23) / 2
n = 12 or n = -11/2
Since the number of guests must be a positive integer, the only valid solution is n = 12.
Therefore, the number of guests in the party is 12.
Let's assume there are n guests in the party.
To find the number of handshakes, we can use the formula n(n-1)/2. (Every guest shakes hands with n-1 other guests, but we divide by 2 because each handshake is counted twice).
According to the problem, the total number of handshakes is 66.
Therefore, we can set up the equation:
n(n-1)/2 = 66
Simplifying this equation gives:
n(n-1) = 132
Expanding the left side of the equation gives:
n^2 - n = 132
Bringing all the terms to one side of the equation gives:
n^2 - n - 132 = 0
Now we can use the quadratic formula to solve for n:
n = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -1, and c = -132.
Plugging these values into the formula gives:
n = (1 ± sqrt(1 - 4(1)(-132))) / 2(1)
Simplifying this equation gives:
n = (1 ± sqrt(529)) / 2
Since we are looking for a positive integer value of n, we can discard the negative solution and simplify further:
n = (1 + 23) / 2 or n = (1 - 23) / 2
n = 12 or n = -11/2
Since the number of guests must be a positive integer, the only valid solution is n = 12.
Therefore, the number of guests in the party is 12.
Community Answer
Every two persons shakes hands with each other in a party and the tota...
NC2 = 66 . n(n-1)/2 = 66 . n(n-1) = 132 .
n(n-1) = 12 × 11 . n= 12
n(n-1) = 12 × 11 . n= 12
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Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14?
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Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14?.
Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is (a) 11 (b) 12 (c) 13 (d) 14?.
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