Question

In a hall, 576 chairs are arranged in row and column with the number of rows equal to the number of columns. The chairs in one row and one column is removed. How many chairs are removed?

• A. $49$
• B. $47$
• C. $57$
• D. $59$

Answer 1

The correct option is B

$47$

Initially, the number of chairs is 576

Since the number of rows is equal to the number of columns, which say is 'a'

We have $a^2=576$

a = $\sqrt[2]{2576}$

a = $\sqrt[2]{22^3\times 3\times 2^3\times 3}$

a = $\sqrt[2]{22^6\times 3^2}$

a = $2^3\times 3$

a = $24$

Now one row and one column is removed.

Hence, the new number of row and column is equal to 24 -1 = 23

The new number of chairs will be equal to ${23}^2$ = 529

Therefore the number of chairs removed is equal to $576-529$ = $47$