Question

In the orange garden of Mr. Madhusudan there are 150 orange trees. The number of trees in each row is 5 more than that in each column. Find the number of trees in each row and each column with the help of following flow chart. 

Answer 1

Let the number of trees in each column be x. 
Number of trees in a row = x + 5
Total trees = Number of rows  \[\times\] Number of columns = \[x\left( x + 5 \right)\] =150 

\[\Rightarrow x\left( x + 5 \right) = 150\]
\[ \Rightarrow x^2 + 5x - 150 = 0\]
\[ \Rightarrow x^2 + 15x - 10x - 150 = 0\]
\[ \Rightarrow x\left( x + 15 \right) - 10\left( x + 15 \right) = 0\]
\[ \Rightarrow \left( x + 15 \right)\left( x - 10 \right) = 0\]
\[ \Rightarrow x = 10, - 15\]

But number of columns cannot be negative so, number of columns = 10. 
Number of rows = 10 + 5 = 15