Question

A boat travels with a speed of 15 km/h in still water. In a river flowing at 5 km/hr; the boat travels some distance downstream and then returns. The ratio of average speed to the speed in still water is -

• A. $8:3$
• B. $3:8$
• C. $8:9$
• D. $9:8$

Answer 1

Answer: (C)

$8:9$

Let ${}^{\prime }{d}^{\prime }$ be the distance traveled by boat in the downstream.
Now, Downstream speed + Speed of boat in still water = Relative speed of boat in downstream.
Relative speed of boat in downstream= $15+5=20km/hr$
Time taken by boat in downstream $t_1$ = Distance traveled by boat in downstream/ Relative speed of boat in downstream
$t_1=\frac{d}{20}hr$
Distance traveled by boat in the upstream is same as downstream i.e. ${}^{\prime }{d}^{\prime }$
Speed of boat in still water- Upstream speed = Relative speed of boat in upstream
Relative speed of boat in upstream= $15-5=10km/hr$
Time taken by boat in upstream $t_2$ = Distance traveled by boat in upstream/ Relative speed of boat in upstream.
$t_2=\frac{d}{10}hr$
So, Average speed = Total distance traveled by boat in both upstream and downstream/Total time taken by boat in both upstream and downstream
Average speed= $\frac{2d}{t_1+t_2}=\frac{2d}{\frac{d}{20}+\frac{d}{10}}$
Average speed= $\frac{40}{3}km/hr$
We have to find the ratio of Average speed : Speed of boat in still water= $\frac{40}{3}:15=8:9$
Hence, option $C$ is the correct answer.