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
Answers
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)
(OR)
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) /2So 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.
Answer:
ANSWER IS 120 persons
Step-by-step explanation:
simply APPLY LOGIC OF SUPER 30
HANDSHAKES = 120
SINCE 120 IS THE NUMBER OF HANDSHAKES NOT THE NUMBER OF HANDS
SO, NUMBER OF HANDS= 120 *2 ( ASSUMING THAT NOBODY IN THE PARTY IS DIFFERENTLY ABLED , EVERYONE HAS 2 HANDS )
= 240 HANDS
AND NOW EACH PERSON HAS 2 HANDS SO NUMBER OF PERSON
= 240/2
= 120 PERSON