Answer: Option A
Let the width of the path be x
Then,
$$\left[ {\left( {38 \times 32} \right) - \left\{ {\left( {38 - 2x} \right)\left( {32 - 2x} \right)} \right\}} \right]$$       $$ = 600$$
$$\eqalign{
& \Rightarrow \left[ {1216 - \left( {1216 - 140x + 4{x^2}} \right)} \right] \cr
& \Rightarrow 4{x^2} - 140x + 600 = 0 \cr
& \Rightarrow {x^2} - 35x + 150 = 0 \cr
& \Rightarrow {x^2} - 30x - 5x + 150 = 0 \cr
& \Rightarrow \left( {x - 30} \right)\left( {x - 5} \right) = 0 \cr
& \Rightarrow x = 5\,m\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\therefore x \ne 30} \right] \cr} $$