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Two friends A and B are stationed at two different points P and Q respectively along the same bank of a straight stretch of a flowing stream. The ratio of the speeds of A and B in still water is 1: 3. When A and B swim in the opposite directions from P and Q respectively, they meet at a point 30 meters from Q. If the time taken by A to reach point Q and B to reach point P from their original positions P and Q is the same, then the distance (in meters) between P and Q is


Options:
A .   45
B .   90
C .   120
D .   60
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:
PQ30x+y=303xy......(1)
And,
PQx+y=PQ3xy.........(2) 
(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
x=y
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.



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