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