In order to reach his office on time, Mr. Roy goes through the middle passage of a round fort which he takes 14 minutes to pass through. However, on a certain day, due to repairs, the straight road being blocked, he had to take the roundabout way as a result of which he reached his office late. How late was he ?

A. 6 min

B. 8 min

C. 12 min

D. 7$$\frac{1}{2}$$ min

Answer: Option B

Solution(By Examveda Team)

Let the diameter of the round fort be D
Distance through the middle passage = D
Roundabout distance = $$\frac{{\pi D}}{2}$$
Time taken to cover distance D = 14 min
Time taken to cover distance :
$$\eqalign{ & = \frac{{\pi D}}{2} \cr & = \frac{{14}}{D} \times \frac{{\pi D}}{2} \cr & = 7\pi \cr & = \left( {7 \times \frac{{22}}{7}} \right)\min \cr & = 22\,\min \cr} $$
∴ Required time difference = (22 - 14) min = 8 min