Arun's speed of swimming in still water is 5 km/hr. He swims between two points in a river and returns back to the same starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 2 km/hr, then the distance between the two points is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1.75 km
$\text{Speed in still water}=5,\;\text{speed of stream}=2.$
$\text{Upstream speed}=5-2=3,\;\text{Downstream speed}=5+2=7.$
$\text{Let distance between two points}=d.$
$\text{Time upstream}=\frac{d}{3},\;\text{Time downstream}=\frac{d}{7}.$
$\frac{d}{3}-\frac{d}{7}=\frac{20}{60}=\frac{1}{3}.$
$d\left(\frac{7-3}{21}\right)=\frac{1}{3}.$
$d\cdot\frac{4}{21}=\frac{1}{3}.$
$d=\frac{1}{3}\cdot\frac{21}{4}=\frac{7}{4}.$
$d=1.75.$
$\text{Distance between the two points}=1.75\text{ km}.$