Question

The students of a class are made to stand in complete 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.

Answer 1

Let the number of rows be x and number of students in a row be y.
Total number of students in the class
= Number of rows x Number of students in a row
= xy
According to the question,
Total number of students = (x - 2) (y + 1)
xy = (x - 2) (y + 1)

Total number of students = (x + 3) (y - 1)
xy =  (x + 3) (y - 1)

Simplify the above two equations to find the values of x and y.

Answer 2

Answer:

60

Step-by-step explanation:

Let the number of students in one row be taken as x

And let the number of rows be taken as y

Then the total number of students = xy

Then according to the first condition given in the problem, we have

(x + 1) (y – 2) = xy

xy – 2x + y – 2 = xy

-2x + y = 2 … (i)

And, according to the second condition given in the problem, we have

(x – 1) (y + 3) = xy

xy + 3x – y – 3 = xy

3x – y = 3 … (ii)

Adding equations (i) and (ii), we get

-2x + y = 2

3x – y = 3

————–

x = 5

On substituting the value of x in equation (i), we have

-2(5) + y = 2

-10 + y = 2

y = 2 + 10

y = 12

Therefore, the number of students = xy = 5 x 12 = 60.