Question

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. Find the number of students in the class.

Answer 1

Given: 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. Find the number of students in the class.

Step-wise calculation:

1. Let the number of rows = r and the number of students in each row = t.

Then total students N = r × t.

2. Case 1 (3 extra in each row, 1 row less):

N = (r – 1)(t + 3)

So r × t = (r – 1)(t + 3) 

⇒ rt = rt + 3r – t – 3 

⇒ 0 = 3r – t – 3

⇒ t = 3r – 3   ...(Equation A)

3. Case 2 (3 less in each row, 2 rows more):

N = (r + 2)(t – 3)

So r × t = (r + 2)(t – 3) 

⇒ rt = rt – 3r + 2t – 6 

⇒ 0 = –3r + 2t – 6 

⇒ 3r = 2t – 6   ...(Equation B)

4. Substitute t from (A) into (B):

3r = 2(3r – 3) – 6

= 6r – 6 – 6

= 6r – 12 

⇒ 3r = 6r – 12

⇒ –3r = –12 

⇒ r = 4

5. Then t = 3r – 3

= 3 × 4 – 3 

= 9

6. Total students N = r × t 

= 4 × 9 

= 36

The number of students in the class is 36.