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Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is?
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Every 2 person shakes hands with eachother in a party and the total nu...
Number of Guests in the Party
Given
- Every 2 persons shake hands with each other.
- Total number of handshakes = 66.
Approach
- Let the number of guests in the party be n.
- Each person shakes hands with n-1 other people.
- So, the total number of handshakes = n*(n-1)/2 (as each handshake involves 2 people).
Solving the Equation
- From the given information, we have n*(n-1)/2 = 66.
- Solving this equation, we get n^2 - n - 132 = 0.
- Factoring this quadratic equation, we get (n-12)(n+11) = 0.
- So, n = 12 or n = -11. Since the number of guests cannot be negative, n = 12.
Conclusion
- Therefore, the number of guests in the party is 12.
Given
- Every 2 persons shake hands with each other.
- Total number of handshakes = 66.
Approach
- Let the number of guests in the party be n.
- Each person shakes hands with n-1 other people.
- So, the total number of handshakes = n*(n-1)/2 (as each handshake involves 2 people).
Solving the Equation
- From the given information, we have n*(n-1)/2 = 66.
- Solving this equation, we get n^2 - n - 132 = 0.
- Factoring this quadratic equation, we get (n-12)(n+11) = 0.
- So, n = 12 or n = -11. Since the number of guests cannot be negative, n = 12.
Conclusion
- Therefore, the number of guests in the party is 12.
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Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is?
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Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is?.
Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Every 2 person shakes hands with eachother in a party and the total number of handshake is 66.the number of guests in the party is?.
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