Question

A boat takes $19$ hours for travelling downstream from point $A$ to point $B$ and coming back to a point $C$ midway between $A$ and $B$. If the velocity of the stream is $4$ $kmph$ and the speed of the boat in still water is $14kmph,$ what is the distance between $A$ and $B$?

• A. $160km$
• B. $180km$
• C. $200km$
• D. $220km$

Answer 1

The correct option is B $180km$

Speed in downstream = $(14+4)km/hr=18km/hr;$

Speed in upstream = $(14–4)km/hr=10km/hr.$

Let the distance between A and B be $x$ km. Then,

$\frac{x}{18}+\frac{x}{2}\times \frac{1}{10}$ = 19

$\Rightarrow \frac{x}{18}+\frac{x}{20}$ = 19

$\Rightarrow$ $x=180km.$