Subject: General Aptitude · Chapter: Area · Exam: 2007 · Marks: · Difficulty:
A path of uniform width runs round the inside of a rectangular field 38 m long and 32 m wide. If the path occupies $600 \mathrm{m}^{2}$, then the width of the path is
(a)5 m
(b)10 m
(c)18.75 m
(d)30 m
Answer
Answer (as printed): A
Explanation
Let the width of the path be $x$. Then, $[(38 \times 32)-\{(38-2 x)(32-2 x)\}]=600$ $$\begin{aligned} & \Rightarrow\left[1216-\left(1216-140 x+4 x^{2}\right)\right] \\ & \Rightarrow 4 x^{2}-140 x+600=0 \Rightarrow x^{2}-35 x+150=0 \\ & \Rightarrow x^{2}-30 x-5 x+150=0 \Rightarrow(x-30)(x-5)=0 \\ & \Rightarrow x=5 \mathrm{m} . \quad[\therefore x \neq 30] \end{aligned}$$