Question

In a hall, 324 chairs are arranged in such a way that the number of rows is equal to the number of columns. If one extra row and one extra column of chairs is added, find the new number of the chairs.

• A. 324
• B. 361
• C. 381
• D. 376

Answer 1

The correct option is B

361

Initially since number of rows is equal to number of columns, it is forming a square.

Let the number of rows be ${}^{\prime }{a}^{\prime }$ and Let the number of columns be ${}^{\prime }{a}^{\prime }$

Total number of chainrs $=a^2$

$\therefore a^2=324$

$a=\sqrt{324}$

$a=\sqrt{2\times 2\times 3\times 3\times 3\times 3}$

$a=\sqrt{2^2\times 3^4}$

$a=2\times 3^2=18$

So, there are 18 rows and 18 columns of chairs.

Now, if we add 1 row and 1 column, the number of rows and columns become 19.

Now the total number of chainrs will be $=19\times 19={19}^2=361$