| A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30 m/min, then the radius of the circular ground is \[\left( \text{take}\,\,\pi =\frac{22}{7} \right).\] |
| [SSC (CGL) 2013] |
A) 10.5 cm
B) 3.6 m
C) 5.5 m
D) 7.5 m
Correct Answer: B
Solution :
| 1st the radius of circular field \[=r\,m\] |
| Speed of person in \[m/s=\frac{30}{60}=\frac{1}{2}m/s\] |
| According to the question, |
| \[\frac{2\pi r}{1/2}-\frac{2r}{1/2}=30\]\[\Rightarrow \]\[4\pi r-4r=30\] |
| \[\Rightarrow \]\[\left( 4\times \frac{22}{7}-4 \right)r=30\] |
| \[\Rightarrow \]\[(12.5-4y)r=30\] |
| \[\Rightarrow \] \[(8.5)r=30\] |
| \[\therefore \] \[r=\frac{30}{8.5}=3.5\,\,m\] |
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