question_answer

The speed of a boat in still water is 16 km/hr and the speed of the current is 4 km/hr. It lakes a total of 7.5 hours to row upstream from Point P to Q and downstream from Point Q to R. If the distance between P and R is one-fifth the distance between Q and R then what is the distance between Q to R? (Where QR <PQ)

A)  97 km             

B)  42.23 km

C)  84.46 km                     

D)  48.64 km

E)  None of these

Correct Answer: E

Solution :

Let the distance from Q to R be x km. \[\therefore \] P to \[R=\frac{x}{5}\] Upstream speed = 16 - 4 = 12 km/hr Downstream speed = 16 + 4 = 20 km/hr Now-\[\frac{6x}{5\times 12}+\frac{x}{20}=7.5\Rightarrow \frac{6x}{5\times 12}+\frac{x}{20}=7.5\]\[\Rightarrow \frac{x}{10}+\frac{x}{20}=7.5\Rightarrow 3x=7.5\times 20\] \[\therefore 50Km\]