Question

A school collected Rs. 2601 as fees from its students. If the fee paid by each student and number of students in school were equal, how many students were there in the school?

Answer 1

The number of students in the school and the fees paid by them are the same. Now take the number of students as $x$ then the fee collected from each student will be $x$ , therefore multiplication of this $x$ with $x$ will give us the total fees collected.

Complete step-by-step answer:

It is said that a school collects the total fees as Rs. 2601.
It is said that the fees paid by each student and the number of students are equal.

 Total amount = number of students \[\times \] amount paid by each student.
Let us consider the number of students as x. As the number of students and amount paid are same, the amount paid by each student is also ‘x’.
\[\therefore \] Total amount \[=x.x\]
\[\begin{align}
  & 2601={{x}^{2}} \\
 & \therefore x=\sqrt{2601} \\
\end{align}\]
Let us solve this by prime factorization. The integer factorization of a composite number into a product of smaller integers, and if three factors are prime numbers, then it is called prime factorization.
Prime numbers have only 1 and itself as a factor.
\[\begin{align}
  & \therefore 2601=3\times 3\times 17\times 17 \\
 & 2601={{3}^{2}}\times {{17}^{2}} \\
 & \therefore x=\sqrt{2601} \\
 & x=\sqrt{{{3}^{2}}\times {{17}^{2}}}=3\times 17=51. \\
\end{align}\]
Thus we got x = 51.
So the number of students in the school = 51.
The amount paid by each student is Rs. 51.

Note: It is important that you take ‘x’ common as the number of students and amount paid are the same. You might think that Rs. 2601 is paid by one single student. So read the question carefully as it is the total amount paid by all the students studying in the school.