Question

while arranging certain students of a school rows containing equal number of student.if three rows are reduced then three more student have to arranged in each the remaining rows .if three rows are formed then two student have to taken off from each previously row .find the number of student arranged?​

Answer 1

Let the number of students in each row be x .

Let the number of rows be y .

∴ Total number of students = x y

If 3 rows are reduced , row becomes y - 3 .

If 3 students are increased , x becomes x + 3 .

x y = ( x + 3 )( y - 3 )

⇒ x y = x y - 3 x + 3 y - 9

⇒ - 3 x + 3 y - 9 = 0

⇒ y - x - 3 = 0 .........( 1 )

If 3 rows are increased , row becomes y + 3 .

If 2 students are decreased , x becomes x - 2 .

⇒ x y = ( x - 2 )( y + 3 )

⇒ x y = x y + 3 x - 2 y - 6

⇒ 3 x - 2 y - 6 = 0

⇒ 2 y - 3 x + 6 = 0 .....( 2 )

Multiplying ( 1 ) with 2 we get :

⇒ 2 y - 2 x - 6 = 0 .....( 3 )

Subtract 2 and 3 :

⇒ - 2 x + 3 x  - 6 - 6 = 0

⇒ x = 12

Neglect the negative value of x  :

Take x =  12

2 y - 2 x - 6 = 0

⇒ 2 y - 24 - 6 = 0

⇒ 2 y - 30 = 0

⇒ 2 y = 30

⇒ y = 30/2

⇒ y = 15

Number of students = x y

= 12 × 15

⇒ 180 .

180 students were there .

Answer 2

Question

while arranging certain students of a school rows containing equal number of student.if three rows are reduced then three more student have to arranged in each the remaining rows .if three rows are formed then two student have to taken off from each previously row .find the number of student arranged?

Answer

There are 12 students in each row.

There are 15 rows in total.

And total no.of students arranged =

No. of row × no. of students in each row

=>15×12

=>180

Hence there were 180 students in total.

Plz refer to the attachment for explanation.

Thanks