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 ( Take = 227 ):

Answer: Option D

Solution

Answer: Option D

Solution:

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

$$\begin{array}{rl}& 2\pi R-2R=15\\ & 2R\left(\pi -1\right)=15\\ & 2R=\frac{15}{\pi -1}\\ & 2R=\frac{15}{\frac{22}{7}-1}\\ & 2R=\frac{15\times 7}{15}\\ & 2R=7\\ & R=\frac{7}{2}\\ & R=3.5\text{ m}\end{array}$$