Question

Students of class VIII have decided to deposit some money for the welfare of rural students. Each student contributed the sum as the number of students of the class. If the total collection was Rs. 2304, then Find the number of students in the class. What amount did each student submit?​

Answer 1

Answer:

Step-by-step explanation:

It is given that

Amount collected for welfare of rural students  =Rs2304

We know that

No. of Student + no. of rupees contributed by each student =

$\sqrt{2304\\}$

​

Here

It can be written as

=

$\sqrt{2*2*2*2*2*2*2*2*3*3}$

​

By further calculation

=2×2×2×2×34=48

Therefore, the number of students in class VIII is 48

Amount submitted by each student is Rs.48

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

• Students of class VIII have decided to deposit some money for the welfare of rural students.

• Each student contributed the sum as the number of students of the class.

Let assume that

• Number of students in class VIII be x

So,

• Amount contributed by each student = Rs x

According to statement

• The total amount collected is Rs 2304

It means

$\rm :\longmapsto\:x \times x = 2304$

$\rm :\longmapsto\: {x}^{2} = 2304$

$\rm \implies\:x = \sqrt{2304}$

Now, we have to evaluate the square root of 2304.

There are two methods to evaluate the square root.

1. Prime Factorization Method

2. Long Division Method

So, using Prime factorization method, we have

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:2304 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:1152\:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:576\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:288\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:144\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:72 \:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:36\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:18\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:9\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:3 \:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

So,

$\rm \implies\: \sqrt{2304} = 2 \times 2 \times 2 \times 2 \times 3$

$\bf \implies\: \sqrt{2304}= 48$

Or

Using Long Division Method

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:48 \:\:}}}\\ {\underline{\sf{4}}}& {\sf{\:\:2304 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \:16  \:    \:  \: \:\:}} \\ {\underline{\sf{88}}}& {\sf{\:\: \: \: \: 704   \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 704 \:  \:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: 0\:\:\:}} \end{array}\end{gathered}\end{gathered}$

$\bf \implies\: \sqrt{2304}= 48$

Hence,

• Amount submitted by each student is Rs 48.