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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.
Solution
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.
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