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

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## 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.

Video Solution
Pair Of Linear Equations In Two Variables
Ex 3.7 | Question 4

## 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, $$xy = 4 \times 9 = 36$$

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