Question

The students of Class VIII of a school donated \(Rs.~2401\) in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Answer 1

Given:

Donated money $Rs.2401$

Let the number of students be $x$.
$\Rightarrow$ Money donated by each student $=x$.

According to the question,

$x\times x=2401$

$\Rightarrow x^2=2401$

$\Rightarrow x=\sqrt{2401}$

$\begin{array}{cc}7& 2401\\ 7& 343\\ 7& 49\\ 7& 7\\ & 1\end{array}$

$\Rightarrow \sqrt{2401}=\sqrt{7\times 7\times 7\times 7}$

$\Rightarrow \sqrt{2401}=\sqrt{49\times 49}$
$\Rightarrow \sqrt{2401}=49$

Hence, the number of students in the class VIII is $49$.