Question

Students of a school were made to stand in rows for drill. If 3 students less were standing in each row, 10 more rows would be required and if 5 students more were standing in each row, then the number of rows would be reduced by 10. Find the number of students participating in the drill.

Answer 1

Let the no . of students standing in each row be x and let no. of rows be y.

∴ Total no. of students participating in the drill = xy 

As per the first given condition,

               (x - 3 )(y + 10 ) = xy 

 ∴ x (y + 10) - 3 (y + 10 ) = xy 

 ∴        xy + 10x - 3y - 30 = xy 

∴                        10x - 3y = 30              .....................(1)

    As per the second given condition,

              (x + 58 ) (y-10) = xy 

∴  x(y - 10) + 5(y - 10 ) = xy 

∴       xy - 10x + 5y -50 = xy 

∴                  -10x + 5y = 50                 ..........................(2)

Adding (i) and (ii),

                     10x - 3y = 30 

                   -10x + 5y = 50

_______________________________

                              2y = 80

∴                             y = `80/2`

∴                             y = 40

           Substituting y = 40 in (i) , 

              10x  - 3 (40) = 30

∴               10x - 120 = 30

∴                        10x = 30 + 120

∴                        10x = 150

∴                           x = `150/10`

∴                            x = 15 

∴         xy = 15 × 40 = 600

∴ 600 students were participating in the drill.