A boat can cover a certain distance upstream in $16$ minutes and the same distance in still water in $12$ minutes. The time taken to cover the same distance downstream is:

Question

A boat can cover a certain distance upstream in $16$ minutes and the same distance in still water in $12$ minutes. The time taken to cover the same distance downstream is:

Option A

8 minutes

Option B

9 minutes

Option C — Correct answer

9.6 minutes

Correct choice.

Option D

10 minutes

Explanation

Let the distance be $D$. Then upstream speed $=\frac{D}{16}$ and still-water speed $=\frac{D}{12}$. So stream speed $=\frac{D}{12}-\frac{D}{16}=\frac{D}{48}$. Downstream speed $=\frac{D}{12}+\frac{D}{48}=\frac{5D}{48}$, giving time $=\frac{D}{5D/48}=\frac{48}{5}=9.6$ minutes.

Chapter Mock 9: Boat and Stream