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.

Answer 1

Answer:

Let the number of rows be A and the number of students in a row be B.

Total number of students = Number of rows x Number of students in a row

=AB

Using the information, that is given,

First Condition:

Total number of students = (A – 1) ( B + 3)

Or AB = ( A – 1 )(B + 3) = AB – B + 3A – 3

Or 3A – B – 3 = 0

Or 3A – Y = 3 – – – – – – – – – – – – – (1)

Second condition:

Total Number of students = (A + 2 ) ( B – 3 )

Or AB = AB + 2B – 3A – 6

Or 3A – 2B = -6 – – – – – – – – – (2)

When equation (2) is subtracted from (1)

(3A – B) – (3A – 2B) = 3 – (-6)

-B + 2B = 3 + 6B = 9

By using the equation (1) we get,

3A – 9 =3

3A = 9+3 = 12

A = 4

Number of rows, A = 4

Number of students in a row, B = 9

Number of total students in a class = AB = 4 x 9 = 36

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Answer 2

Answer:

Let the number of rows be x

Number of students in 1 row = y

According to the question,

(y + 3) (x - 1) = xy xy + 3x - y - 3 = xy

Or 3x - y = 3 ...(1)

(y - 3) (x + 2) = xy xy - 3x + 2y - 6 = xy

Or -3x + 2y = 6 ...(2)

Adding (1) and (2), we get,

y = 9

3x - 9 = 3 x = 4

Number of students = xy = 4 9 = 36