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
:
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:
PQ−30x+y=303x−y......(1)
And,
PQx+y=PQ3x−y.........(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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