Question

The students of a class are made to stand in rows. If $3$ students are extra in a row, there would be $1$ row less. If $3$ students are less in a row, there would be $2$ rows more. Find the number of students in the class.

Answer 1

Let the number of rows be $R$

The number of students in a row be $S$.

Total number of students = Number of rows x Number of students in a row$=RS$

As per the given data

First Condition:

Total number of students $=(R–1)(S+3)$

$$\begin{gathered} RS=(R–1)(S+3)=RS–S+3R–3 \\ 3R–S–3=0 \\ 3R–Y=3 \end{gathered}$$

Second condition:

Total Number of students $=(R+2)(S–3)$

$$\begin{gathered} RS=RS+2S–3R–6 \\ 3R–2S=-6 \end{gathered}$$

When equation (ii) is subtracted from (i)

$$\begin{gathered} (3R–S)–(3R–2S)=3–(-6) \\ -S+2S=3+6S=9 \end{gathered}$$

By using the equation (i) we get,

$\begin{array}{rcl}3R–9& =& 3\\ 3R& =& 9+3\\ & =& 12\\ R& =& 4\end{array}$

Number of rows, $R=4$

Number of students in a row, $S=9$

Number of total students in a class$=RS=4x9=36$

Hence, the number of students in the class is $36$.