Question

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Class X students assembled for a meeting were made to stand in rows. If 4 students were less in a row, there would be 3 more rows. Whereas if 8 students were more in a row, there would be 3 less rows. Find the number of students in the class

Answer 1

Assuming that the no. of students in each row would be same and the students are arranged as the following:

$----------------\\----------------\\----------------\\----------------\\----------------\\----------------\\----------------\\----------------$

Means here the students are arranged in row and column, so that the no. of students is the product of no. of students in a row and that in a column.

And also, the no. of students in a column is equal to the no. of rows, and that of students in a row is equal to the no. of columns.

Let the no. of students in a row be x and the no. of rows be y. So that the total no. of students will be xy.

1. Given that there would be 3 more rows if 4 students from each row were less. But the total no. of students wouldn't change. Replacement of students were occurring here. So,

$(x-4)(y+3)=xy \\ \\ xy+3x-4y-12=xy \\ \\ 3x-4y-12=0 \\ \\ 3x-4y=12\ \ \ \longrightarrow\ \ \ (1)$

2. Given that there would be 3 less rows if 8 students were more in each row. Here also the total no. of students wouldn't change. So,

$(x+8)(y-3)=xy \\ \\ xy-3x+8y-24=xy \\ \\ -3x+8y-24=0 \\ \\ -3x+8y=24 \\ \\ 3x-8y=-24 \\ \\ 3x-4y-4y=-24 \\ \\ 12-4y=-24\ \ \ \ \ [\text{From (1) }]\\ \\ 4y=12+24\\ \\ 4y=36\\ \\ y=9$

From (1),

$3x-4y=12\\ \\ 3x-4(9)=12 \\ \\ 3x-36=12 \\ \\ 3x=12+36 \\ \\ 3x=48 \\ \\ x=16$

Hence the total no. of students is xy = 16 × 9 = 144.

Answer 2

Answer:

144

Step-by-step explanation: