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Question
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.
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 = (x − 1) (y + 3) = xy − y + 3x − 3
3x − y − 3 = 0
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
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