The students of a school are made to stand in rows. If the number of students in each row is increased by 6, there would be 4 row less. If the number of students in each rows is reduced by 6, there would be 5 rows more. Find the number of students in the school.


Answer:

2160

Step by Step Explanation:
  1. Let us assume that there are x students in each row and y rows in total.

    Thus, the total number of students in the school is xy.
  2. If the number of students in each row is increased by 6, then the number of rows becomes (y4).

    As the total number of students remain same, we have xy=(x+6)(y4)xy=xy4x+6y24[ Cancelling xy ]4x6y=24(i)
  3. If the number of students in each row is reduced by 6, then the number of rows becomes (y+5).
  4. Adding \text{eq(i)} and \text{eq(ii)}, we get \begin{aligned} {\implies}& (4 - 5) x = (-24 -30) \\ {\implies}& -x = -54 \\ {\implies}& x = 54 \end{aligned}
  5. Substituting the value of x in \text{eq(i)}, we get \begin{aligned} &4 \times 54 - 6 y = -24 \\ {\implies} & - 6 y = -24 - 216 \\ {\implies} & - 6 y = -240 \\ {\implies} & y = 40 \end{aligned}
  6. Therefore, the total number of students in the school = xy = 54 {\times} 40 = 2160.

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