A boat moves downstream at the rate of 1 km in 71/2 minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in the still water?

Answer: Option B

Rate downstream of boat
$$\begin{array}{rl}& \text{ = }\left(\frac{1}{\frac{15}{2\times 60}}\right)\text{kmph}\\ & =\frac{2\times 60}{15}\text{kmph}\\ & =8\text{kmph}\end{array}$$
Rate downstream of boat = 5 kmph
Speed of boat in still water = $$\frac{1}{2}$$ (Rate downstream + Rate upstream)
$$\begin{array}{rl}& =\frac{1}{2}\left(8+5\right)\\ & =\frac{13}{2}\\ & =6\frac{1}{2}\text{kmph}\end{array}$$