The speed of the current is 5 km/h. A motorboat goes 10 km upstream and back again to the starting point in 50 min. The speed, (in km/h) of the motorboat in still water is?

Let speed of boat be x km/h.
Given speed of current = 5 km/h
∴ Upstream speed of boat = (x -5) km/h
Downstream speed of boat = (x + 5) km/h
According to the question.
10/(x - 5) + 10/(x + 5) = 50/60
⇒ 10(x + 5 + x - 5)/( x² - 25) = 5/6
⇒ x² -24x - 25 = 0
⇒ x² - 25x + x - 25 = 0
⇒ (x - 25) (x + 1) = 0
∴ x = 25 [∴ x ≠ -1]