Let the number of students in a row be ‘a’ and number of rows be ‘b’.
Given,
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.
Number of students remain constant .
⇒ ab = (a + 3)(b – 1) ab = (a – 3)(b + 2)
So,
ab = ab - a + 3b - 3a - 3b = - 3 ...... (1)
and
ab = ab + 2a - 3b - 62a - 3b = 6 ...... (2)
Subtract 1 from 2 to get,
2a - 3b - (a - 3b) = 6 - (- 3)2a - 3b - a + 3b = 6 + 3a = 9
Put the value of a in 1 to get,
9 - 3b = - 3 - 3b = - 3 - 9 - 3b = - 12b = 4
Solving the above equations we get,
a = 9 and b = 4
Thus, number of students = ab = (9)(4) = 36