Question

An army general arranges his soldiers in such a way that the number of
rows is same as number of columns. In such an arrangement 55 soldiers
are left behind. If the total number of soldiers are 3419, find the number
of soldiers in each row.

Answer 1

Dear student,

$$\begin{gathered} Letthenumberofsoldiersineachrowbex \\ thennumberofsoldiersineachcolumnsbex \\ Thetotalnumberofsoldiersinthearrangement=no.ofrows\times no.ofcolumns \\ Theremainingsoldiersandthesoldiersinthisformation=6455 \\ thustheeqnbecomes \\ \Rightarrow x^2+55=6455 \\ \Rightarrow x^2=6455-55 \\ \Rightarrow x^2=6400 \\ \Rightarrow x=\sqrt{6400} \\ \Rightarrow x=\pm 80 \\ neglecting-vesign \\ therefore,numberofsoldiersineachrowis80. \end{gathered}$$

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