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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.


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Solution

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=(x1)(y+3)
xy=xyy+3x3
3xy=3(i)
Condition 2
Total number of students = (x+2) (y-3)
xy=xy+2y3x6
3x2y=6(ii)
Subtracting equation (ii) from (i)
(3xy)(3x2y)=3(6)
y+2y=3+6
y=9
By using equation (i), we obtain
3x - 9 = 3
3x9+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


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