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

Therefore, Upstream speed of boat = (x-5) km/h

Downstream speed of boat = (x + 5) km/h

According to the question,

\( \Large \frac{10}{x-5}+\frac{10}{x+5}=\frac{50}{60} \)

\( \Large 10 \left(\frac{x+5+x-5}{x^{2}-25}\right)=\frac{5}{6} \)

\( \Large 12 \times 2x = x^{2}-25 \)

\( \Large x^{2}-24x-25=0 \)

\( \Large x^{2}-25x+x-25=0 \)

\( \Large \left(x-25\right) \left(x+1\right)=0 \)

Therefore, x = 25 \( \Large \left[because, x \ne -1\right] \)