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 $\mathrm{B}=$ $\frac{\text{ distance travelled in downstream }}{\text{ speed of boat in downstream }}=\frac{AB}{18}$ $=\frac{x}{18}\mathrm{h}$
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
$\therefore \frac{x}{18}+\frac{x}{20}=19$
$\Rightarrow \frac{10x+9x}{180}=19$
$\Rightarrow \frac{19x}{180}=19\Rightarrow x=180\mathrm{km}$
$\therefore \text{ Distance between }A\text{ and }C\text{ in }$
$\frac{x}{2}=\frac{180}{2}=90\mathrm{km}$