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The students of a class are made to stand equally in rows. If $3$ students are extra in each row, there would be $1$ row less. If $3$ students are less in a row, there would be $2$ more rows. Find the number of students in the class.
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Sol. Let number of students in each row be $x$ and the number of rows be $$\begin{aligned}& y \\ & \therefore\end{aligned}$$ Total number of students $$\begin{aligned}& = xy \\ & ATQ, (x + 3)(y - 1) = xy \\ & \Rightarrow x - 3y + 3 = 0\end{aligned}$$ Also, $$\begin{aligned}& (x - 3)(y + 2) = xy \\ & \Rightarrow 2x - 3y - 6 = 0\end{aligned}$$ On solving these equations, we get
$x = 9$ and $$\begin{aligned}& y = 4 \\ & \therefore\end{aligned}$$ Number of students in the class $= xy = 9 \times 4 = 36$
$x = 9$ and $$\begin{aligned}& y = 4 \\ & \therefore\end{aligned}$$ Number of students in the class $= xy = 9 \times 4 = 36$