Question

A boat takes 11 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream be 3 km/hr and the speed of the boat in still water be `12 km/hr, then what is the distance between A and B ?

• A. $100$ km
• B. $90$ km
• C. $110$ km
• D. $120$ km

Answer 1

The correct option is B $90$ km

Speed of downstream = (12 + 3) km/hr = 15 km/hr

Speed upstream = ( 12 - 3) km/hr = 9 km/hr

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

$\frac{x}{15}+\frac{\frac{x}{2}}{9}=11\Rightarrow \frac{x}{15}+\frac{x}{18}=11$

$\Rightarrow \frac{6x+5x}{90}=11\Rightarrow \frac{11x}{90}=11\Rightarrow x=90km$