An army general arranges his soldiers in such a way that the number of rows is the same as the number of columns. In doing so, he finds that $55$ soldiers are left out. If the total number of soldiers is $6455$ , find the number of soldiers in each row.

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Solution

Total number of soldiers $= 6455$
Number of soldiers left out $= 55$
Let the number of rows $= x$
Let the number of columns $= x$
Number of soldiers remained $= 6455 - 55 = 6400$
Now, No. of soldiers remained $=$ No. of columns $\times$ No. of rows
$x^{2} = 6400$
$\Rightarrow x = \sqrt{6400}$
$\Rightarrow x = 80$
Number of columns and number of rows $= 80$

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An army general arranges his soldiers in such a way that the number of rows is the same as the number of columns. In doing so, he finds that 55 soldiers are left out. If the total number of soldiers is 6455, find the number of soldiers in each row.

Total number of soldiers =6455Number of soldiers left out =55Let the number of rows =xLet the number of columns =xNumber of soldiers remained =6455−55=6400Now, No. of soldiers remained = No. of columns × No. of rows x2=6400⇒x=√6400⇒x=80Number of columns and number of rows =80

An army general arranges his soldiers in such a way that the number of rows is the same as the number of columns. In doing so, he finds that $55$ soldiers are left out. If the total number of soldiers is $6455$ , find the number of soldiers in each row.