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 the number of rows and columns increased by 1. If there are 625 soldiers now, how many soldiers were added?

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Solution

The correct option is B
49

Number of rows and columns when there are 625 soldiers = $\sqrt{625}$ = $\sqrt{25 \times 25}$ = 25

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

$∴$ , initial number of soldiers $24^{2}$ = 576

$∴$ number of soldiers added = 625 - 576 = 49

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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 the number of rows and columns increased by 1. If there are 625 soldiers now, how many soldiers were added?

The correct option is B 49 Number of rows and columns when there are 625 soldiers = √625 = √25×25 = 25 ⇒ Intial number of rows and columns = 25 -1 = 24 (As one more row and column was added) ∴, initial number of soldiers 242 = 576 ∴ number of soldiers added = 625 - 576 = 49