A boat goes 4 km upstream and 4 km downstream in 1 hour. The same boat goes 5 km downstream and 3 km upstream in 55 minutes. What is the speed (in km/hr) of boat in still water?

Let speed of boat in still water = $$x$$ km/hr and speed of current = $$y$$ km/hr

The boat goes 4 km upstream and 4 km downstream in 1 hour

Using, time = distance/speed

=> $$\frac{4}{x+y}+\frac{4}{x-y}=1$$

Similarly, $$\frac{5}{x+y}+\frac{3}{x-y}=\frac{55}{60}$$

Let $$\frac{1}{x+y}=w$$ and $$\frac{1}{x-y}=z$$

=> $$4w+4z=1$$ and $$5w+3z=\frac{55}{60}$$

Solving above equations, we get : $$w=\frac{1}{12}$$ and $$z=\frac{1}{6}$$

=> $$x+y=12$$ ---------(i)

and $$x-y=6$$ -----------(ii)

Adding equations (i) and (ii), => $$2x=12+6=18$$

=> $$x=\frac{18}{2}=9$$ km/hr

=> Ans - (C)