Question

Students of a school were made to stand in rows for drill. If 3 students less were standing in each row, 10 more rows were required and if 5 students more were standing in each row then the number of rows was reduced by 10. Find the number of students participating in the drill.

Answer 1

Let the number of rows be x.
Number of students in each row = y
Then total number of students = xy
Now, according to the question, we have:
$$\begin{gathered} \left(x+10\right)\left(y-3\right)=xy \\ \Rightarrow xy-3x+10y-30=xy \\ \Rightarrow -3x+10y=30...\left(1\right) \\ \mathrm{Also},\left(x-10\right)\left(y+5\right)=xy \\ \Rightarrow xy+5x-10y-50=xy \\ \Rightarrow 5x-10y=50...\left(2\right) \\ \mathrm{Adding}\mathrm{eqs}.\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{get}: \\ -3x+10y=30 \\ \underline{5x-10y=50} \\ 2x=80 \\ \Rightarrow x=40 \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get}: \\ -3\times 40+10y=30 \\ \Rightarrow -120+10y=30 \\ \Rightarrow 10y=30+120 \\ \Rightarrow 10y=150 \\ \Rightarrow y=15 \end{gathered}$$

∴ Number of students participating in the drill = $xy=40\times 15=600$