The speed of a motorboat in still water and that of the current of water is in a ratio of 27 : 5. The boat goes along the current from point A to point B in 3 hours 40 minutes. How much time will it take to come back from B to A?

5 hours 20 minutes

The correct answer is Option (1) → 5 hours 20 minutes

Speed of boat in still water : speed of stream $=27:5$

Let speed of boat in still water $=27k$ and speed of stream $=5k$

Speed downstream $=27k+5k=32k$

Speed upstream $=27k-5k=22k$

Time downstream $=3$ hours $40$ minutes $=\frac{11}{3}$ hours

Distance between $A$ and $B$

$=32k\times\frac{11}{3}=\frac{352k}{3}$

Time upstream

$=\frac{\text{distance}}{\text{speed upstream}}=\frac{\frac{352k}{3}}{22k}$

$=\frac{352}{66}=\frac{176}{33}$ hours

$=\frac{176}{33}$ hours $=5\frac{11}{33}$ hours

$=5$ hours $20$ minutes

The time taken to return from $B$ to $A$ is $5$ hours $20$ minutes.