Q. The speed of the current is 5 km/hr. A motorboat goes 10 km upstream and back again to the starting point in 50 minutes. The speed (in km/hr) of the motorboat in still water is :
Answer: 25
Notes: Let the speed of motorboat in still water be x km/hr. $latex \therefore \frac{10}{x-5}+\frac{10}{x+5} = \frac{50}{60}&s=1$ $latex => 10\left ( \frac{x+5+x-5}{(x+5)(x-5)} \right )= \frac{5}{6}&s=1$ $latex => 20x\times 6 = (x^{2}-25)\times 5$ $latex => x^{2}-24x-25 = 0$ $latex => x^{2}-25x+x-25 = 0$ $latex => x(x-25)+1(x-25)= 0$ $latex => (x-25)(x+1) = 0$ $latex => x = 25$ Hence speed of motorboat in still water is 25 km/hr. Hence option [C] is correct answer.