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
- 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. -
If the number of students in each row is increased by 6, then the number of rows becomes (y−4).
As the total number of students remain same, we have xy=(x+6)(y−4)⟹xy=xy−4x+6y−24[ Cancelling xy ]⟹4x−6y=−24…(i) - If the number of students in each row is reduced by 6, then the number of rows becomes (y+5). ∴
- 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}
- 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}
- Therefore, the total number of students in the school = xy = 54 {\times} 40 = 2160.