Question

There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to the number of columns. How many children would be left out in this arrangement?

Answer 1

Hint: In this question we first need to find a number less than or equal to 500 that is the perfect square of a number. After finding that number we will subtract it from 500 and we will get the desired number of students.

Complete step by step answer:
500 children for a P.T. drills have to stand in such a manner that the number of rows is equal to the number of columns.
Let the number of rows be x
We are given that the number of rows is equal to number of columns
So, number of columns =x
Total number of students in x rows and x columns = x.x
 As total number of students in a drill would be less than or equal to 500
Mathematically we can express it as:
\[\begin{array}{l}
 \Rightarrow x \times x \le 500\\
 \Rightarrow {x^2} \le 500\\
 \Rightarrow x \le \sqrt {500} \\
 \Rightarrow x \le 22.36
\end{array}\]As x is number of rows that cannot be in fraction so greatest acceptable value of x is 22
So, Number of rows = 22 = number of columns
So, Number of students in arrangement = 22×22 = 484
No. of children would be left out in this arrangement = 500 - 484 = 16

Hence, 16 children would be left out in this arrangement.

Note: In this type of questions we need to take care of one thing that is acceptable value of x would be 22 not 23. After squaring 22 we need to subtract it from 500.