Question

Aman Verma and Mini Mathur jointly host a TV programme in which one day n guests attended the show. There each guest shakes hands with every other guest and each guest has to shake hand with each of the hosts. If there happens to be total 65 shake hands, find the number of guests attended the show.

Answer 1

Number of guests attending the show = n given.

It is given each guest shakes hands with every other guest and each guest has to shake hand with each of the hosts.There were  total 65 shake hands

N number of people have 2n hand shakes with Aman Verma and Mini Mathur .

Number of handshakes for n number of people - 2n = 65

$\frac{n(n-1)}{2}-2n=65.$

$n^{2}$-n+4n=130.

(n+13)(n-10)=0

Or n=-13 or n=10

Number of people can not be a negative number .Number of guests present =10.

Answer 2

n(n-1) /2 +2n=65

n^2-n+4n=130

n^2+3n-130=0

by solving this equation using quadratic equation

n=-13 (or)n=10