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In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.
a) 14
b)15
c)21
d)22?
a) 14
b)15
c)21
d)22?
Most Upvoted Answer
In a party every person shakes hands with every other person. if there...
Understanding Handshakes
In a party, if every person shakes hands with every other person, the total number of handshakes can be calculated using the combination formula. The formula for the number of handshakes (H) in a group of n people is:
H = n(n - 1) / 2
In this scenario, we know there are 105 handshakes.
Setting Up the Equation
To find the number of persons (n), we can set up the equation:
n(n - 1) / 2 = 105
Now, let's solve for n.
Multiplying Both Sides
1. Multiply both sides by 2:
n(n - 1) = 210
Rearranging the Equation
2. Rearranging gives us:
n^2 - n - 210 = 0
Factoring the Quadratic
3. To factor this quadratic equation, we look for two numbers that multiply to -210 and add up to -1. These numbers are 14 and -15.
Thus, we can factor the equation as:
(n - 15)(n + 14) = 0
Finding the Roots
4. The roots of this equation are:
n - 15 = 0 → n = 15
n + 14 = 0 → n = -14 (not valid since n cannot be negative)
Conclusion
The number of persons in the party is:
- 15
Therefore, the correct answer is option (b) 15.
In a party, if every person shakes hands with every other person, the total number of handshakes can be calculated using the combination formula. The formula for the number of handshakes (H) in a group of n people is:
H = n(n - 1) / 2
In this scenario, we know there are 105 handshakes.
Setting Up the Equation
To find the number of persons (n), we can set up the equation:
n(n - 1) / 2 = 105
Now, let's solve for n.
Multiplying Both Sides
1. Multiply both sides by 2:
n(n - 1) = 210
Rearranging the Equation
2. Rearranging gives us:
n^2 - n - 210 = 0
Factoring the Quadratic
3. To factor this quadratic equation, we look for two numbers that multiply to -210 and add up to -1. These numbers are 14 and -15.
Thus, we can factor the equation as:
(n - 15)(n + 14) = 0
Finding the Roots
4. The roots of this equation are:
n - 15 = 0 → n = 15
n + 14 = 0 → n = -14 (not valid since n cannot be negative)
Conclusion
The number of persons in the party is:
- 15
Therefore, the correct answer is option (b) 15.
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In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.a) 14b)15c)21 d)22?
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In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.a) 14b)15c)21 d)22? 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 In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.a) 14b)15c)21 d)22? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.a) 14b)15c)21 d)22?.
In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.a) 14b)15c)21 d)22? 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 In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.a) 14b)15c)21 d)22? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a party every person shakes hands with every other person. if there are 105 handshakes in total, find the number of persons in the party.a) 14b)15c)21 d)22?.
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