A person can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream?

Solution (By Examveda Team)

Let the speeds of boat and stream was $$s$$ and $$v$$ km/hr respectively
Then, Actual Speed Downstream = $$\left(s + v\right)$$  km/hr
Actual Speed upstream = $$\left(s - v\right)$$  km/hr
According to question,
$$\eqalign{ & \frac{d}{{s + v}} + \frac{d}{{s - v}} = 5\,{\text{hr}}{\text{.}}\,15\,{\text{min}}{\text{.}} \cr & \Rightarrow \frac{d}{{s + v}} + \frac{d}{{s - v}} = \frac{{21}}{4}\,.\,.....\left( 1 \right) \cr & {\text{and}} \cr & \frac{{2d}}{{s - v}} = 7 \cr & \Rightarrow \frac{d}{{s - v}} = \frac{7}{2}\,......\left( 2 \right) \cr & {\text{By equation }}\left( 1 \right) - \left( 2 \right), \cr & \frac{d}{{s + v}} = \frac{{21}}{4} - \frac{7}{2} \cr & \Rightarrow \frac{d}{{s + v}} = \frac{{21 - 14}}{4} \cr & \Rightarrow \frac{d}{{s + v}} = \frac{7}{4} \cr & \Rightarrow \frac{{2d}}{{s + v}} = \frac{7}{2} \cr & \cr} $$
Hence, he takes $$\frac{{7}}{{2}}$$ hours to row 2d km distance downstream