(B) 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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(B) 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$$y = 5$Substituting $y = 5$ in equation $(1)$:$x - 2(5) = 2$$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

Medium

While arranging the students of standard $X$ in rows,if two rows are reduced,then one more student has to be arranged in each of the remaining rows. If three more rows are formed,then one student has to be taken off from each of the previously arranged rows. Find the total number of students in the class.

A
$23$
B
$60$
C
$63$
D
$32$

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

Is it true to say that the pair of equations $-x + 2y + 2 = 0$ and $\frac{1}{2}x - \frac{1}{4}y - 1 = 0$ has a unique solution? Justify your answer.

Medium

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If $4x - 12y = 20$,then $5x - 15y = \ldots$

Easy

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From the pair of equations $x + 2y = 8 \dots(1)$ and $3x - 4y = -6 \dots(2)$,the first equation should be multiplied by ............. to eliminate $y$.

Easy

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Solve the following pairs of equations by the cross-multiplication method:
$0.5x + 0.3y = 0.1$
$0.6x + 0.3y = 0.3$

Medium

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Places $A$ and $B$ are $90\, km$ apart from each other on a highway. $A$ car starts from $A$ and another from $B$ at the same time. If they move in the same direction,they meet in $9$ hours and if they move in opposite directions,they meet in $\frac{9}{7}$ hours. Find the speeds of the cars.

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Is it true to say that the pair of equations $-x + 2y + 2 = 0$ and $\frac{1}{2}x - \frac{1}{4}y - 1 = 0$ has a unique solution? Justify your answer.

If $4x - 12y = 20$,then $5x - 15y = \ldots$

From the pair of equations $x + 2y = 8 \dots(1)$ and $3x - 4y = -6 \dots(2)$,the first equation should be multiplied by ............. to eliminate $y$.

Solve the following pairs of equations by the cross-multiplication method:$0.5x + 0.3y = 0.1$$0.6x + 0.3y = 0.3$

Places $A$ and $B$ are $90\, km$ apart from each other on a highway. $A$ car starts from $A$ and another from $B$ at the same time. If they move in the same direction,they meet in $9$ hours and if they move in opposite directions,they meet in $\frac{9}{7}$ hours. Find the speeds of the cars.

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Solve the following pairs of equations by the cross-multiplication method:
$0.5x + 0.3y = 0.1$
$0.6x + 0.3y = 0.3$