Question

The members of a club used to meet for lunch on every Monday. It was customary to divide the bill equally. One
Monday, two of the members were called for an official meeting just before the bill was presented. As a result, the
remaining members had to settle the bill of US $ 360 by paying US $ 6 more than each would have otherwise paid.
Find the number of club members?​

Answer 1

Answer:

Let x is the no of members

Each should pay (360/x)

That day there are (x-2) members left just after lunch before payment.

Now each pays 360/(x-2), which is 6 more than (360/x)

Thus, 360/(x-2)-6=360/x

⇒(360-6x+12)/(x-2)= 360/x

⇒x(360-6x+12)=(x-2)360

⇒ -6x²+372x=360x-720

⇒6x²-12x-720=0

⇒x²-2x-120=0

⇒x²-12x+10x-120=0

⇒x(x-12)+10(x-12)=0

⇒(x-12)(x+10)=0

⇒x=12 or -10

Since no of people must be a positive integer so x= 12.

Thus there would be 12 members in the club.(Ans)

Step-by-step explanation: