Answer: Option D
:
D
Let the speeds of A and B be x m/s and 3x m/s respectively and let the speed of the stream br y m/s.
According to the question:
$\frac{PQ-30}{x+y}=\frac{30}{3x-y}......\left(1\right)$
And,
$\frac{PQ}{x+y}=\frac{PQ}{3x-y}.........\left(2\right)$
(If we assume the water flows in the direction Q to P,then 3x+y=x-y, which is not possible.)
From (2),we get:
3x-y=x+y
$\Rightarrow$x=y
$\Rightarrow$Substituting in (1),we get : PQ=60 m.
Shortcut Method :
As time taken by A and B is the same to cover equal distances in opposite direction,means effective speeds of both the friends are the same . Hence, distances between P and Q =30+30 = 60 metres.