# Ex.3.7 Q4 Pair of Linear Equations in Two Variables Solution - NCERT Maths Class 10

## 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.

## Text Solution

**What is Known?**

Changes in number of students in a row and number of rows.

**What is Unknown?**

Number of students in the class.

**Reasoning:**

Assume number of rows equal to *\(x\)* and number of students in each row be \(y.\) Then the total number of students in the class can be calculated by;

Total number of students \( =\) Number of rows \(\times\) Number of students in each row

**Steps:**

Let the number of rows be \(x\)

And number of students in each row be \(y\)

Then the number of students in the class be \(xy\)

Using the information given in the question,

**Condition 1 **If \(3\) students are extra in a row, there would be \(1\) row less

\[\begin{align}\left( {x - 1} \right)\left( {y + 3} \right) &= xy\\xy + 3x - y - 3 &= xy\\3x - y &= 3 \qquad \quad \left( 1 \right)\end{align}\]

**Condition 2 **If 3 students are less in a row, there would be \(2\) rows more

\[\begin{align}\left( {x + 2} \right)\left( {y - 3} \right) &= xy\\xy - 3x + 2y - 6 &= xy\\ - 3x + 2y &= 6 \qquad \quad \left( 2 \right)\end{align}\]

Adding equations \((1)\) and \((2),\) we obtain \(y = 9\)

Substituting \(y = 9\) in equation \((1),\) we obtain

\[\begin{align}3x - 9 &= 3\\3x &= 12\\x &= 4\end{align}\]

Hence, number of students in the class, \(xy = 4 \times 9 = 36\)