The ratio of the speed of a boat to that of the current water is 35 : 8. The boat goes along with the current in 5 hours 10 minutes. What will be the time taken by the boat to come back?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8 hours 13 minutes 48 seconds.
Let's denote the speed of the boat in still water as B and the speed of the current as C.
Given, B:C = 35:8
We can assume B = 35x and C = 8x, where x is a constant.
⇒ Downstream Speed (with the current): B + C = 35x + 8x = 43x
⇒ Upstream Speed (against the current): B - C = 35x - 8x = 27x
Given: Time taken to go downstream = 5 hours 10 minutes = 31/6 hours
⇒ Distance covered downstream: Distance = Speed × Time = 43x × (31/6)
To find the time taken to go upstream:
⇒ Time = Distance / Speed = (43x × 31/6) / 27x
⇒ Time = (43 × 31) / (6 × 27) = 1333 / 162 hours
Converting this to hours and minutes:
⇒ 1333 / 162 = 8 hours + (37/162) hours
Approximating (37/162) hours to the nearest minute:
⇒ (37/162) × 60 ≈ 14 minutes
Therefore, the time taken by the boat to come back (upstream) is approximately 8 hours 14 minutes.