Question

There are 104 students in class 10 and 96 students in class 9 in a school. In a house examination the students are to be evenly seated in parallel rows such that no 2 adjacent rows are of the same class. Find the maximum number of parallel rows of each class for the seating arrangement. Also find the number of students in class 9 and also class 10 in a row.

Answer 1

Hint: We will first find the HCF between 96 and 104 to get the maximum number of parallel rows of each class. Then to find the number of students in class 9 and class 10 in a row we will divide the total number of students in class 9 and class 10 by the calculated HCF.

Complete step-by-step answer:

Number of students in class 10 \[=104\]

Number of students in class 9 \[=96\]

We get the total number of students \[=96+104=200\]

So in the question it has been asked to find the maximum number of parallel rows of each class and thus we will find the HCF between 96 and 104.

HCF is the highest common factor.

So factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48.

And factors of 104 are 1, 2, 4, 8, 13, 26, 52.

So the highest common factor between 96 and 104 is 8.

Hence the maximum number of parallel rows of each class is 8 rows.

Now we have to find the number of students in class 9 and class 10 in a row. For this we will divide the total number of students in class 9 and class 10 by 8.

Number of class 9 students in a row \[=\dfrac{96}{8}=12\].

Number of class 10 students in a row \[=\dfrac{104}{8}=13\].


Note: Just remember that whenever a question is asked and two numbers are given we will directly calculate the highest common factor between those two numbers. Also keep in mind that in the question number of students of class 10 is given first but in the later part number of students in a row of class 9 is asked first, so in a hurry we may write the number of students in a row of class 9 in place of class 10.