Q. 44.1( 146 Votes )

# 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 :

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

Total students of the class = Number of rows x Number of students in a row = *xy*

Using the information given in the question,

**Condition 1**

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

*x*- 1) (

*y*+ 3)

=

*xy*-

*y*+ 3

*x*- 3

3*x* - *y* - 3 = 0

3*x* - *y* = 3 ....(*i*)

**Condition 2**

Total number of students = (*x* + 2) (*y* - 3)

= *xy* + 2*y* - 3*x* - 6

⇒3*x* - 2*y* = -6 ... (*ii*)

Subtracting equation (*ii*) from (*i*),

(3*x - y*) - (3*x* - 2*y*) = 3 - (-6)

⇒- *y* + 2*y* = 9

⇒3 + 6 *y* = 9

By using equation (*i*), we obtain 3*x* - 9 = 3,

⇒3*x* = 9 + 3

⇒3x *= 12⇒ x = 4*

⇒ 3

*(4)*-

*y*= 3

⇒ 12 - y = 3

⇒ 9 = y

Number of rows = *x* = 4

Number of students in a row = *y* = 9

Number of total students in a class = Number of students in 1 row × Number of rows*= xy*

= 4 x 9 **= 36**

Rate this question :

Solve the following pair of linear equation by cross - multiplication method:

x + 4y + 9 = 0

5x – 1 = 3y

KC Sinha - Mathematics