question_answer

A can go round a circular path 8 times in 40 min, If the diameter of the circle is increased to 10 times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is   

A)                         25 min

B)  20 min  

C)  50 min

D)  100 min

Correct Answer: C

Solution :

Circumference \[=2\pi r=\frac{44}{7}\times r\,\,\text{m}\]

Distance covered in 8 times \[=16\pi r\,\,\text{m}\]

\[\therefore \]      \[\text{Speed=}\frac{\text{Distance}}{\text{Time}}\]

\[=\frac{16\pi r}{40}\,\,\text{m/}\min \]

\[=\frac{2\pi r}{5}\,\,\text{m/}\min \]

New circumference \[=2\pi r\times 10\pi =20\pi r\]

\[\therefore \] Required time\[=\frac{20\pi r}{2\pi r}\times 5\min \]

= 50 min