Question

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.

Answer 1

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 $560+840=\boxed{1400}$

Answer 2

Answer:

People =560 and money donated by Chief =₹1400