The ratio of speeds of a motor boat and that of current of water is 35:6. The boat goes against the current in 6 hours 50 minutes. The time taken by boat to come back is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4 hours 50 minutes
Let the speed of the boat in still water be 35k and the speed of the current 6k. Then
upstream speed \(= 35k - 6k = 29k\)
downstream speed \(= 35k + 6k = 41k\)
The distance is the same both ways, so the time is inversely proportional to the speed. The upstream time is 6 hours 50 minutes = 410 minutes:
\( \displaystyle \text{time back} = 410 \times \frac{29k}{41k} = 10 \times 29 = 290 \text{ minutes} \)
\(290 \text{ minutes} = 4 \text{ hours } 50 \text{ minutes}\)