Question

In school auditorium the number of chair in row is same as the number of rows of chair. There are 7033 students in school if we know that less than 31 chairs were empty how many chairs were empty after all students sat down

Answer 1

let chairs in row be x

so number of rows also , x

total number of chairs = x * x

= x^2

there are 7033 students in school and each student gets chair . some chairs leaves empty

so , x^2 > 7033 , such that x^2 is not exceeds than 7033 + 31 = 7064

so finding the square number just below 7064

80^2 = 6400

90^2 = 8100

the number is between 80 and 90

now 85^2 = 7225

so expected number is below 85

83^2 = 6889
84^2 = 7056

so x^2 = 7056 = 84^2

which is total number of chairs in auditorium

so 7056 - 7033 = 23

23 chairs remains empty