Question

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 cloud affairs

Answer 1

Answer:

16 people

Step-by-step explanation:

If there are n people, there will be n(n - 1)/2 handshakes

Find n, given that there are 120 handshakes

n(n - 1)/2 = 120

n(n - 1) = 240

n² - n - 240 = 0

(n - 16) (n + 15)  = 0

n = 16 or n = - 15 (rejected, since number of people cannot be negative)

Answer: There are 16 people at the affair

Answer 2

Answer:

16

Step-by-step explanation:

Given In party there is a total of 120 handshakes. If all the persons shakes hand with every other person.

Let number of persons be n.

The first person will shake hands with (n - 1) people.

Second person will hand shake with (n - 2) people,(since first person has already shaken hands with him and there are now n - 2 people).

and so on till n is reached,

hence the number of handshakes will be:

(n -1) + (n - 2) + (n - 3) +-----------------+ 1

We know that 1 + 2 + 3 +-------------+ n = n(n + 1) /2

Therefore, 1 + 2 + ---------------------+ (n -1) = (n -1) (n -1 + 1) /2 = n(n - 1) /2

So n(n - 1) / 2 = 120

   n^2 - n = 240

 n^2 - n - 240 = 0

n = - b ± √b^2 - 4ac / 2a

n = - (-1) ± √(-1)^2 - 4 (-1)(-240) / 2(1)

n = 1 ± √961 / 2

n = 1 ± 31 / 2

n = 32 / 2

n = 16  ignoring negative, since number of people cannot be negative.