Question

An army base has some soldiers, such that when they stand in rows and columns they form a square. More soldiers were added to the camp and now the number of rows and columns increased by 1. If there are 625 soldiers now, how many soldiers were added?

• A. 64
• B. 49
• C. 69
• D. 54

Answer 1

The correct option is B

49

Number of rows and columns when there are 625 soldiers = $\sqrt{625}$

Prime factorisation of 625 is
$625=5\times 5\times 5\times 5$

So, $\sqrt{625}=\sqrt{\underset{–}{5\times 5}\times \underset{–}{5\times 5}}$
$\Rightarrow \sqrt{625}=5\times 5=25$

$\therefore$ Number of rows and columns when there are 625 soldiers = 25

$\Rightarrow$ Intial number of rows and columns = 25 -1 = 24 (As one more row and column was added)

$\therefore$ initial number of soldiers = ${24}^2$ = 576

$\therefore$ number of soldiers added =
625 - 576 = 49