A person observed that he required 30 seconds less time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30 m/minutes. then the radius of the circular ground is $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right):$$

Solution (By Examveda Team)

Distance covered in 30 seconds = 30 m/min × $$\frac{{30}}{{60}}$$ = 15 m
This is the difference of distance of the boundary and the diameter.
Let 'R' be the radius

$$\eqalign{ & 2\pi R - 2R = 15 \cr & 2R\left( {\pi - 1} \right) = 15 \cr & 2R = \frac{{15}}{{\pi - 1}} \cr & 2R = \frac{{15}}{{\frac{{22}}{7} - 1}} \cr & 2R = \frac{{15 \times 7}}{{15}} \cr & 2R = 7 \cr & R = \frac{7}{2} \cr & R = 3.5{\text{ m}} \cr} $$