The speed of a boat in still water is 12 km/hr. It takes twice as long as to go upstream to a point as to return downstream to the starting point , then the speed of the stream is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 km/hr
Let the speed of the stream be s km/hr. Then the upstream speed is 12 − s and the downstream speed is 12 + s.
For the same distance, time is inversely proportional to speed. Since the upstream trip takes twice as long:
\( \displaystyle \frac{12+s}{12-s}=2 \)
\( \displaystyle 12+s=24-2s \)
\( \displaystyle 3s=12 \)
\( \displaystyle s=4 \)
The speed of the stream is 4 km/hr.
Shortcut: Check Option (3): upstream 8 km/hr, downstream 16 km/hr; downstream is twice as fast, so upstream takes twice as long.
CBSE Applied Mathematics (Class XII):
Boats and Streams
