A boat covers 720 km downstream in 12 hours and covers a certain distance upstream in 15 hours. The ratio of the distance travelled by the boat downstream and upstream is 6:5. Find the taken by the boat to cover 122km in still Water.

Correct option is B

​$$\textbf{Given:} \\\text{Downstream distance} = 720 \text{ km}, \quad \text{Time} = 12 \text{ hours} \\\Rightarrow \text{Downstream speed} = \frac{720}{12} = 60 \text{ km/h} \\[10pt]\text{Let upstream distance} = x \text{ km}, \quad \text{Time} = 15 \text{ hours} \\\Rightarrow \text{Upstream speed} = \frac{x}{15} \\[10pt]\text{Given: Ratio of downstream to upstream distance} = 6:5 \\\Rightarrow \frac{720}{x} = \frac{6}{5} \Rightarrow x = \frac{720 \times 5}{6} = 600 \text{ km} \\[10pt]\Rightarrow \text{Upstream speed} = \frac{600}{15} = 40 \text{ km/h} \\[10pt]\text{Speed in still water} = \frac{\text{Downstream speed} + \text{Upstream speed}}{2} \\= \frac{60 + 40}{2} = 50 \text{ km/h} \\[10pt]\text{Time to cover 122 km in still water} = \frac{122}{50} = \boxed{2.44 \text{ hours}}$$​​