The speed of a boat in still water is 16 km/h. The times taken by the boat to cover the same distance upstream and downstream are in the ratio \(5 : 3\). What is the speed of the stream?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4 km/h
For the same distance, time is inversely proportional to speed. So if the times upstream and downstream are in the ratio \(5 : 3\), the speeds upstream and downstream are in the ratio \(3 : 5\).
Let the speed of the stream be y km/h:
\( \displaystyle \frac{16 + y}{16 - y} = \frac{5}{3} \)
\(48 + 3y = 80 - 5y\)
\(8y = 32\)
\(y = 4\)
Check: upstream speed 12 km/h and downstream speed 20 km/h are in the ratio \(3 : 5\).