(D) Let the number of rows be $x$ and the number of students in each row be $y$. The total number of students is $xy$.According to the first condition

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(D) Let the number of rows be $x$ and the number of students in each row be $y$. The total number of students is $xy$.According to the first condition: $(x - 2)(y + 1) = xy$$xy + x - 2y - 2 = xy$$x - 2y = 2$ --- $(1)$According to the second condition: $(x + 3)(y - 1) = xy$$xy - x + 3y - 3 = xy$$-x + 3y = 3$ --- $(2)$Adding equations $(1)$ and $(2)$:$(x - 2y) + (-x + 3y) = 2 + 3$$y = 5$Substituting $y = 5$ into equation $(1)$:$x - 2(5) = 2$$x - 10 = 2$$x = 12$Total number of students $= xy = 12 \times 5 = 60$.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

Difficult

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

A
$12$
B
$30$
C
$36$
D
$60$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

Find the value$(s)$ of $p$ for the pair of equations $-x + py = 1$ and $px - y = 1$ if the system has no solution.

Difficult

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If $\frac{x}{2} = \frac{6}{y} = 2$,then the value of $x - y$ is ..........

Easy

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If $\frac{5}{x}+\frac{3}{y}=4$ and $\frac{3}{x}+\frac{5}{y}=2,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

Medium

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Which of the following groups matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1. x+2y=3, 2x+4y=5$ $a. \text{Solution set is a singleton set.}$

$2. 2x+3y=6, x+\frac{3}{2}y=3$ $b. \text{Solution set is an empty set.}$

$3. 3x-y=0, x-y+6=0$ $c. \text{Solution set is an infinite set.}$

$d. \text{Solution set contains two members.}$

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The age of the father is twice the sum of the ages of his two children. After $20$ years,his age will be equal to the sum of the ages of his children. Find the age of the father (in years).

Medium

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Part $I$	Part $II$
$1. x+2y=3, 2x+4y=5$	$a. \text{Solution set is a singleton set.}$
$2. 2x+3y=6, x+\frac{3}{2}y=3$	$b. \text{Solution set is an empty set.}$
$3. 3x-y=0, x-y+6=0$	$c. \text{Solution set is an infinite set.}$
	$d. \text{Solution set contains two members.}$

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

Similar Questions

Find the value$(s)$ of $p$ for the pair of equations $-x + py = 1$ and $px - y = 1$ if the system has no solution.

If $\frac{x}{2} = \frac{6}{y} = 2$,then the value of $x - y$ is ..........

If $\frac{5}{x}+\frac{3}{y}=4$ and $\frac{3}{x}+\frac{5}{y}=2,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

The age of the father is twice the sum of the ages of his two children. After $20$ years,his age will be equal to the sum of the ages of his children. Find the age of the father (in years).

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