Question

students of school were made to stand in rows for drill. if 3 students less were standing in each row, 10 more rows were required and if 5 students more were standing in each row then the number of rows was reduced by 10. Find the numbers of students participating in the drill.​

Answer 1

Number of students in participating in drill = 600

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Answer 2

Step-by-step explanation:

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

So, the total number of students = xy.

(i)

3 students less were standing in each row. 10 more rows were required.

⇒ (y - 3)(x + 10) = xy

⇒ xy + 10y - 3x - 30 = xy

⇒ -3x + 10y = 30

⇒ 3x - 10y = -30   ------ (1)

(ii)

Given, 5 more students were standing then the numbers of rows were reduced by 10.

⇒ (y + 5)(x - 10) = xy

⇒ xy - 10y + 5x - 50 = xy

⇒ 5x - 10y = 50    ------ (2)

On solving (1) & (2), we get

⇒ 3x - 10y = -30

⇒ 5x - 10y = 50

   -------------------

    -2x = -80

       x = 40.

Substitute x = 40 in (1), we get

⇒ 3x - 10y = -30

⇒ 3(40) - 10y = -30

⇒ 120 - 10y = -30

⇒ -10y = -30 - 120

⇒ y = 15.

Therefore, number of students = xy = 600.

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