The speed of a boat in still water is 15 km/hr. It takes twice as long as to go upstream to a point as to return downstream to the starting point. The speed of the stream is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 km/hr
Let the speed of the stream be s km/hr and the distance be d km. The upstream speed is 15 − s and the downstream speed is 15 + s.
\( \displaystyle \frac{d}{15-s}=2\cdot\frac{d}{15+s} \)
\( \displaystyle 15+s=2(15-s) \)
\( \displaystyle 15+s=30-2s \)
\( \displaystyle 3s=15\ \Rightarrow\ s=5\text{ km/hr} \)
Shortcut: For the same distance, time is inversely proportional to speed, so the downstream speed is twice the upstream speed: with s = 5, 20 = 2 × 10.