Students of a class are made to stand in rows | vedclass

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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 conditi

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(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 $= xy = 12 	imes 5 = 60$. Wait,checking the options provided,there seems to be a discrepancy. Let us re-evaluate the calculation.
If $x=12, y=5$,total $= 60$. If $1$ extra student per row ($6$ per row),rows $= 60/6 = 10$ (which is $12-2=10$). Correct.
If $1$ less student per row ($4$ per row),rows $= 60/4 = 15$ (which is $12+3=15$). Correct.
The calculated answer is $60$. Since $60$ is not in the options,let us re-read the question. If the question implies $x$ students per row and $y$ rows,the logic holds. Given the options,perhaps the question intended different values. However,based on the provided logic,the result is $60$.

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.

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