Question

Question 4
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

Answer 1

Let the number of rows be x and number of students in a row be y.
Total students of the class = Number of rows $\times$ number of students in a row
= xy
Using the information given in the question,
Condition 1
Total number of students = (x-1)(y+3)
$\Rightarrow xy=(x-1)(y+3)$
$\Rightarrow xy=xy-y+3x-3$
$\Rightarrow 3x-y=3\left(i\right)$
Condition 2
Total number of students = (x+2) (y-3)
$xy=xy+2y-3x-6$
$3x-2y=-6\left(ii\right)$
Subtracting equation (ii) from (i)
$(3x-y)-(3x-2y)=3-(-6)$
$\Rightarrow -y+2y=3+6$
$\Rightarrow y=9$
By using equation (i), we obtain
3x - 9 = 3
$\Rightarrow 3x-9+3=12$
$\Rightarrow x=4$
Number of rows = x = 4
Number of students in a row = y = 9
Number of total students in a class $=xy=4\times 9=36$