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In party there is a total of 120 handshakes. If all the persons shakes hand with every other person. Then find the number of person present in the party.
- a)15
- b)16
- c)17
- d)18
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In party there is a total of 120 handshakes. If all the persons shakes...
Let person A be the one moving from aurangabad and N moving from Ellora
Lets say they meet at a point C which is x km away from aurangabad and (28 - x) km away from Ellora.
The distance covered by A is x Km and by B is (28 - x) km.
This is covered in 1 hrs so the speed for :
A = x km/h
B = (28 - x) km / h
A has (28 - x) km to cover whereas B has x km more to cover.
Since we have the distance and the speeds for the two, we can get the time taken to reach respective destinations.
A :(28 - x) / x
B :x /(28 - x)
We know that A arrives 35 minutes later which is equivalent to 7 / 12 hrs
Putting this in an equation form we have :
x / (28 - x) + 7/12 = (28 - x) / x
Expanding the equation we get :
12 x^2 + 196 x - 7x^2 = 9408 - 672x + 12x^2
Collecting like terms together :
- 7x^2 + 868 x - 9408 = 0
Dividing through by a negative :
7x^2 - 868 x + 9408 = 0
Solving for X using the quadratic formula we have :
X = {868 +/-√(868x^2 - 4 x7 x 9408)} / (2 x 7)
X = {868 +/- (700)} / 14
X = 12 or 112
We pick 12 since 112 is more than the total distance thus it is unrealistic.
Speed of B is :
(28 - 12) = 16
16 m / s
Most Upvoted Answer
In party there is a total of 120 handshakes. If all the persons shakes...
Given, the total number of handshakes is 120.
Let the number of persons present in the party be n.
We know that each person shakes hand with every other person.
Calculation:
The number of handshakes can be calculated as follows:
Total number of handshakes = nC2
nC2 = 120
n! / ((n-2)! * 2!) = 120
n * (n-1) = 240
n^2 - n - 240 = 0
(n-16) (n+15) = 0
Therefore, n = 16 or -15.
Since the number of persons cannot be negative, the number of persons present in the party is 16.
Answer: The correct option is (b) 16.
Let the number of persons present in the party be n.
We know that each person shakes hand with every other person.
Calculation:
The number of handshakes can be calculated as follows:
Total number of handshakes = nC2
nC2 = 120
n! / ((n-2)! * 2!) = 120
n * (n-1) = 240
n^2 - n - 240 = 0
(n-16) (n+15) = 0
Therefore, n = 16 or -15.
Since the number of persons cannot be negative, the number of persons present in the party is 16.
Answer: The correct option is (b) 16.
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Community Answer
In party there is a total of 120 handshakes. If all the persons shakes...
If A shakes hand with B then B also shakes hand with A which means that AB+BA forms one group and one hand shake
so there are 120 hand shake In total..
if each group comprises of 2 handshake than than total hand shakes of all the individual are 120*2 handshakes = 240
taking Lcm 240 = 16*15 hence 16 persons in total
so there are 120 hand shake In total..
if each group comprises of 2 handshake than than total hand shakes of all the individual are 120*2 handshakes = 240
taking Lcm 240 = 16*15 hence 16 persons in total
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In party there is a total of 120 handshakes. If all the persons shakes hand with every other person. Then find the number of person present in the party.a)15b)16c)17d)18e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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