The time taken by a boat to go 18 km downstream is equal to the time taken by it to go 10.8 km upstream. The speed of the boat in still water is 8 km/h. How much time (in hours) will the boat take to go 45 km upstream?

Correct option is A

​$$\textbf{Given:} \\\text{Downstream distance} = 18 \text{ km} \\\text{Upstream distance} = 10.8 \text{ km} \\\text{Speed in still water} = 8 \text{ km/h} \\\textbf{Concept Used:} \\\text{Boat and stream problems} \\\textbf{Formula Used:} \\\text{Time} = \frac{\text{Distance}}{\text{Speed}} \\\textbf{Solution:} \\\text{Speed downstream} = 8 + x \\\text{Speed upstream} = 8 - x \\\frac{18}{8 + x} = \frac{10.8}{8 - x} \\18(8 - x) = 10.8(8 + x) \\144 - 18x = 86.4 + 10.8x \\57.6 = 28.8x \\x = 2 \\\text{Upstream speed} = 8 - 2 = 6 \\\text{Time} = \frac{45}{6} = 7.5 \\\textbf{Final Answer:} \\7.5 \text{ hours}$$​​