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

Answer: Option C

Let original diameter be d metre
Then, its circumference = $$\left(\pi d\right)$$ metres
Time taken to cover $$\left(8\pi d\right)$$ m = 40 min
New diameter = $$\left(10d\right)$$ m
Then, its circumference = $$\left(\pi \times 10d\right)$$ m
∴ Time taken to go round it once :
$$\begin{array}{rl}& =\left(\frac{40}{8\pi d}\times 10\pi d\right)\min \\ & =50\min \end{array}$$