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: 36

Step-by-step explanation:

X be the number of rows and Y be the number of students in a row

XY=(X-1)(Y+3) =(X+2)(Y-3)

So 3X-Y=3 and 2Y-3X=6

So Y=9 and X = 12/3 = 4

XY = 4*9 = 36

Answer 2

C O N C E P T :

★ This question We can use the property that the number of students in a class is equal to multiplication of number of rows and number of students in each row ,also the number of students in a class remains the same.

★ first construct the equations according to given conditions as above then simplify these equations and calculate the values of number of rows and number of students in a particular row, then multiply these two values we will get the required number of students in the class.

S O L U T I O N :

Let the number of rows be x and number of students in a row be y.

Total students of the class

= Number of rows × Number of students in a row

= xy

Using the information given in the question,

★ Condition 1

➽Total number of students = (x − 1) (y + 3)

➽ xy= (x − 1) (y + 3) = xy− y + 3x − 3

➽ 3x − y − 3 = 0

➽ 3x − y = 3 (i)

★ Condition 2

➽ Total number of students = (x + 2) (y − 3)

➽ xy= xy+ 2y − 3x − 6

➽ 3x − 2y = −6 (ii)

★ Subtracting equation (ii) from (i),

➽ (3x − y) − (3x − 2y) = 3 − (−6)

➽ − y + 2y = 3 + 6

➽ y = 9

★ By using equation (i), we obtain

➽ 3x − 9 = 3

➽ 3x = 9 + 3 = 12

➽ x = 4

➽ Number of rows = x = 4

➽ Number of students in a row = y = 9

➽ Number of total students in a class = x y= 4 × 9 = 36

∴ The total students in a class is 36