Question

There is Exam being held in the hall of Ravi's school in a few days. He has to arrange chairs for all the students participating in the exam. There would be 9801 students participating in the exam and he has to arrange the chairs in such a way that there are equal numbers of chairs in each row and column. How many chairs would be there in each row and column?​

Answer 1

Let the two classes be C1 and C2 and the four rows be R1,R2,R3,R4. There are 16 students in each class. So, there are 32 students. 

According to the given conditions there are two different ways in which 32 students can be seated :

  R1 R2 R3R4  I C1 C2 C1 C2 II C2 C1 C2 C1

Since the seating arrangement can be completed by using any one of these two ways. So, by the fundamental principle of addition, Total no. of seating arrangements

= No. of arrangements in I case + No. of arrangements in II case.

Now, 16 students of class C1 can be seated in 16 chairs in 16P16=16! ways.

And, 16 students of class C2 can be seated in 16 chairs in 16P16=16! ways.

Hence, the total number of seating arrangements=

Answer 2

if the row = column that means the seating arrangement is a square

and in here we know it's area, which is 9801, so x²= 9801

√x²=√9801

x=√9801

x=99

there are 99 chairs in each row and column