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Question -

The students of a class are made to stand in rows. If 3 student 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 -

Let number of rows = x
and number of students in each row = y
Now according to the conditions given
Number of total students = xy
(y + 3)(x – 1) = xy
=> xy – y + 3x – 3 = xy
=>3x – y = 3 …(i)
and (y – 3) (x + 2) = xy
=> xy + 2y – 3x – 6 = xy
=> 2y – 3x = 6 …(ii)
Adding (i) and (ii), y = 9
Substituting the value of y in (i)
3x – 9 = 3
=> 3x = 3 + 9 = 12
=> x = 4
Number of total students = xy = 4 x 9 = 36

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