there are 104 students in class 10th and 96 students in class 9th in a school .in a house examination the students ate to be evenly seated in parallel rows such that no two adjacent rows are of the same class. (a) find the maximum number of parallel rows of each class for the seeating arrangement. (b) also find the number of student of class 9th and also of class 10th in a row (c) what is the objective of the school administration behind such an arrangement

(a) The maximum number of parallel rows of each class for the seating arrangement can be found by finding the greatest common divisor (GCD) of the number of students in each class.

GCD(104, 96) = 8

So, the maximum number of parallel rows for each class is 8.

(b) To find the number of students from each class in a row, we divide the total number of students in each class by the number of rows.

Number of students in Class 10th per row = 104 / 8 = 13
Number of students in Class 9th per row = 96 / 8 = 12

(c) The objective of the school administration behind such an arrangement could be to promote diversity and integration among the students. By having different classes mixed in the same row, students from different backgrounds can interact with each other, fostering a sense of unity and understanding among them. It also prevents the formation of separate cliques or groups based solely on class divisions.

To find the answers to the questions, let's break down the problem step-by-step:

(a) Find the maximum number of parallel rows for each class:
To ensure that no two adjacent rows are of the same class, we need to alternate between rows of class 9 and class 10 students. If we denote rows of class 9 as "9" and rows of class 10 as "10", the possible arrangements in parallel rows could be:
9 10 9 10 9 10 ...
10 9 10 9 10 9 ...
Each arrangement starts with a different class to ensure no adjacent rows are of the same class. Therefore, the maximum number of parallel rows for each class would be the half of the total number of students in that class.

For Class 9th:
Total number of students = 96
Maximum number of rows = 96 / 2 = 48 rows

For Class 10th:
Total number of students = 104
Maximum number of rows = 104 / 2 = 52 rows

(b) Find the number of students of class 9th and 10th in a row:
Since we have equal seating in each row, we can calculate the number of students in a row for each class by dividing the total number of students in that class by the maximum number of rows obtained in part (a).

For Class 9th:
Number of students in a row = Total number of students in Class 9th / Maximum number of rows for Class 9th
Number of students in a row = 96 / 48 = 2 students in a row for Class 9th

For Class 10th:
Number of students in a row = Total number of students in Class 10th / Maximum number of rows for Class 10th
Number of students in a row = 104 / 52 = 2 students in a row for Class 10th

(c) The objective of the school administration behind such an arrangement:
The objective of the school administration might be to foster a diverse environment and encourage interaction between students of different classes. By seating students from different classes in alternate rows, students have the opportunity to interact with and learn from their peers in different classes. This arrangement promotes social interaction, understanding, and a sense of unity among the students.

To find the maximum number of parallel rows for each class in the seating arrangement, we need to determine the greatest common divisor (GCD) of the number of students in each class.

(a) Find the GCD of 104 and 96:
To find the GCD, we can use the Euclidean algorithm. Divide the larger number by the smaller number, then take the remainder. Repeat this process, dividing the previous divisor by the remainder until the remainder becomes zero.

In this case, we have:
GCD(104, 96) = GCD(96, 104 % 96)
= GCD(96, 8)
= GCD(8, 96 % 8)
= GCD(8, 0)
= 8

So, the GCD of 104 and 96 is 8.

Since we need no two adjacent rows to be of the same class, we can arrange the students in rows of 8 for both classes.

(b) Number of students in class 9th and class 10th per row:
Since we have arranged the students in rows of 8, we divide the total number of students in each class by the number of rows to get the number of students per row.

For class 9th:
Number of students in class 9th = 96
Number of rows = 96 / 8 = 12
Number of students in class 9th per row = 96 / 12 = 8

For class 10th:
Number of students in class 10th = 104
Number of rows = 104 / 8 = 13
Number of students in class 10th per row = 104 / 13 = 8

Thus, in each row, there would be 8 students from both class 9th and class 10th.

(c) Objective of the school administration behind such an arrangement:
The objective of the school administration in such a seating arrangement is to promote diversity and interaction among students from different classes. By ensuring that no two adjacent rows are of the same class, the school aims to facilitate cross-class communication and mingling among the students during the house examination. This arrangement can foster a sense of unity and cooperation among the students, helping them learn from each other and integrate better as a school community.

104 = 8*13

96 = 8*12

That should help