People living in a community decided to donate as much money as a number of people in the community but the chief of the community a little more and hence the total money collected was rs.314440/-. Find the maximum number of people living in that community and also find the amount donated by the chief.

1

Answers

2015-05-08T21:14:38+05:30
Let n = maximum number of people living in the community including chief.

If each person donates n, then the total amount collected would be n\times{n}=n^2
Suppose the chief donates c more than the others : 
n^2+c=314440

Notice that the greatest perfect square less than 314440 is 313600=560^2
Therefore,
n^2+c=560^2+840
\implies n=560 and c=840

That means the maximum number of people living in the community is \boxed{560} and the amount donated by the chief is 560+840=\boxed{1400}

0