Question

A boat takes 19 hours for travelling downstream from point $A$ to $B$ and coming back to a point $C$ midway between $A$ and $B$. If the velocity of the stream is $4 \mathrm{~km} / \mathrm{h}$ and the speed of boat in still water in $14 \mathrm{~km} / \mathrm{h}$. What is the distance between $\mathrm{A}$ and $\mathrm{C}$ ?

• A. $180 \mathrm{~km}$
• B. $120 \mathrm{~km}$
• C. $90 \mathrm{~km}$
• D. $150 \mathrm{~km}$

Answer 1

Answer: (C)

Speed of boat in still water, $b=14 \mathrm{~km} / \mathrm{h}$ Speed of stream, $\mathrm{s}=4 \mathrm{~km} / \mathrm{h}$
So, speed of boat in downstream $=\mathrm{b}+\mathrm{s}$
Speed of boat in upstream $=\mathrm{b}-\mathrm{s}=10 \mathrm{~km} / \mathrm{h}$
Let, distance between $\mathrm{A}$ and $\mathrm{B}$ be ' $x$ ' $\mathrm{km}$

Now,
Time taken from $\mathrm{A}$ to $\mathrm{B}=$ $\frac{\text { distance travelled in downstream }}{\text { speed of boat in downstream }}=\frac{A B}{18}$ $=\frac{x}{18} \mathrm{~h}$
Time taken from $B$ to $C$
$=\frac{\text { Distance travelled in upstream }}{\text { Speed of boat in upstream }}$
$ \frac{\frac{x}{2}}{10}=\frac{x}{20} \mathrm{~h}$
Total time taken from $A$ to $B$ and $B$ to $C=$ 19 hours
$ \therefore \frac{x}{18}+\frac{x}{20}=19 $
$ \Rightarrow \frac{10 x+9 x}{180}=19 $
$ \Rightarrow \frac{19 x}{180}=19 \Rightarrow x=180 \mathrm{~km}$
$ \therefore \text { Distance between } A \text { and } C \text { in } $
$ \frac{x}{2}=\frac{180}{2}=90 \mathrm{~km} $