The students of a class are made to stand equally in rows. If 3 students are extra in each row, there would be 1 row less. If 3 students are less in a row, there would be 2 more rows. Then the number of students in the class would be

Given:

Let S be the total number of students in the class.

Let R be the original number of rows.

Let N be the original number of students in each row.

Total students (S) = R × N

Condition 1: If 3 students are extra in each row, there would be 1 row less.

New number of students per row = N + 3

New number of rows = R - 1

Total students (S) = (R - 1) × (N + 3)

Condition 2: If 3 students are less in a row, there would be 2 more rows.

New number of students per row = N - 3

New number of rows = R + 2

Total students (S) = (R + 2) × (N - 3)

Calculations:

From Condition 1:

RN = (R - 1)(N + 3)

RN = RN + 3R - N - 3

0 = 3R - N - 3

⇒ N = 3R - 3 (Equation 1)

From Condition 2:

RN = (R + 2)(N - 3)

RN = RN - 3R + 2N - 6

0 = -3R + 2N - 6

⇒ 3R - 2N = -6 (Equation 2)

Now, substitute Equation 1 into Equation 2:

3R - 2(3R - 3) = -6

3R - 6R + 6 = -6

-3R = -6 - 6

⇒ R = 4

Now, substitute the value of R back into Equation 1 to find N:

N = 3R - 3

N = 3(4) - 3

N = 12 - 3 = 9

Total number of students (S) = R × N = 4 × 9 = 36     

∴ The number of students in the class would be 36.