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there is a farewell party in a college,there are x nos of student who shake hand with every other student there are totally 153 handshakes in that room,find the total no. of students in that room

there is a farewell party in a college,there are x nos of student who shake hand with every other student there are totally 153 handshakes in that room,find the total no. of students in that room

Grade:10

6 Answers

Ansh Agrawal
55 Points
9 years ago
153
Ashwin
41 Points
9 years ago
hi, 
since number of handshakes given = 153 
let no. of students be n,
therfore, number of handshakes = n(n-1)/2 
 
ATQ,
n(n-1)/2 = 153
n2-n = 306
n2-n-306 = 0
n = 18,-17
we reject n = -17 as no. of students cant be negative 
 
therefore there are 18 students 
Nikhil kumar
67 Points
8 years ago
handshakes = 153 so students can be x
so handshakes can be written as {x(x-1)}/2
{x2-x}/2 = 153 =>x2-x = 306 on solving the equation we get x = -17 and 18.
Nikhil kumar
67 Points
8 years ago
as the no. of students of can not be negative so x = 18 is the possible answer
so students are 18
Prajwal Kavad
603 Points
8 years ago
18 students
 
Kalyani Jayachandran Menon
217 Points
8 years ago
There are 18 students in the room.

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