The students of a class are made to stand in rows. If one student is extra in a row there would be 2 rows less and if one student is less in a row there would be 3 rows more. Find the number of students in the class.

Let the total number of rows be x

also the number of students in each row be y.

According to question, if one student is extra in each row there would be 2 rows less, i. e.

⇒ (x – 2)(y + 1) = xy

⇒ xy – 2 – 2y + x = xy

⇒ x – 2y = 2 ……(i)

also, if one student is less in a row there would be 3 rows more, i. e.

⇒ (x + 3)(y – 1) = xy

⇒ xy – x + 3y – 3 = xy

⇒ – x + 3y = 3 ……(ii)

Adding equation (i) and (ii) and solving:

y = 5

putting this in equation (i);

x = 2y + 2

x = 12.

So, the total number of students in class = xy

= 12 × 5 = 60.