Management Aptitude Test Sep 2013 Paper

(b) Let the radius of circular garden be r.

Then, distance covered by crossing the garden diagonally = r + r = 2r
Also, distance covered when man follows the circular path = $\frac{2\mathit{\pi }\mathit{r}}{2}$
(∵ man has to cover half of the circumference of circle)
= πr
Speed of man in m/s = $\frac{90}{60}=\frac{3}{2}$ m/s
Then By condition given in question,
$\frac{\mathit{\pi }\mathit{r}}{3∕2}-\frac{2\mathit{r}}{3∕2}$ = 45
$\frac{2\mathit{\pi }\mathit{r}-4\mathit{r}}{3}$ = 45;
(2π - 4)r = 135
r = $\frac{135}{\left(2\times 3.14-4\right)}=\frac{135}{\left(6.28-4\right)}$
= $\frac{135}{2.28}$ = 59.21m
Then, circumference of grass plot = 2 π r
= 2 x 3.14 x 59.21 = 371.25 m