Question

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

• A. $55$
• B. $30$
• C. $115$
• D. $60$

Answer 1

Answer: (D)

$60$

Let the original number of rows $=x$
Let the original number of students in each row $=y$
Total number of students in class $=$ Number of students $\times$ Number of rows $=xy$
According to problem
Case $1$
Total no of students $=(y+1)(x-2)=xy$
$\Rightarrow xy-2y+x-2$=$xy$
$\Rightarrow x-2y=2$ ...$\left(1\right)$
Case $2$
Total no of students $=(y-1)(x+3)=xy$
$\Rightarrow xy+3y-x-3=xy$
$\Rightarrow x-3y=-3$ ...$\left(2\right)$
Subtracting eq$\left(1\right)$ from eq$\left(2\right)$ we get
$-y=-5$
$\Rightarrow y=5$
Putting the value of $y$ in eq$\left(1\right)$
$x-2\left(5\right)=2$
$\Rightarrow x=12$
Hence we get $x=12$ and $y=5$
Total no. of students $=xy=60$