Question

The ratio of speeds of a motorboat to that of the current of water is 36 : 5. The motorboat goes along with the current in 5 hours 10 minutes. The time required by the motorboat to come back is equal to

• A. 6 hours 50 minutes
• B. 10 hours 20 minutes
• C. 6 hours
• D. 12 hours

Answer 1

The correct option is A 6 hours 50 minutes

Let the common factor of speeds of a motorboat to that of the current of water be x.
Then, the speed of the motorboat = 36x km/h and the speed of the current = 5x km/h.
Motorboat goes along with the current in 5 h 10 m $\frac{10}{60}h=\frac{310}{60}h=\frac{31}{6}h$

Speed of downstream = 36x + 5x = 41x km/h
Speed of upstream = 36x – 5x = 31x km/h
Now, distance covered by downstream

= speed of downstream ' Time taken $=41x\times \frac{310}{6}km$
Similarly, distance covered by upstream is also $41x\times \frac{310}{60}km$

∴ $\therefore \text{Time taken by upstream}=\frac{\text{Distance covered by upstream}}{\text{Speed of upstream}}=\frac{41x\times \frac{31}{6}}{31x}=\frac{41}{6}=6\frac{5}{6}$
= 6h 50 min
Thus, the time required by the motorboat to come back is equal to 6 hours 50 minutes.
Hence, the correct answer is option (1).