# 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.

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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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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