Question
Three towns X, Y, and Z are on a river which flows uniformly. Y is equidistant from X and Z. If a boats man rows from X to Y and back in 10 hours and X to Z in 4 hours, find the ratio of speed of the boats man in still water to the speed of the current.
Answer: Option B
X ———— Y ———— Z
IF ‘D’ IS THE DISTANCE BETWEEN X AND Y, THEN ‘D’ IS THE DISTANCE BETWEEN Y AND Z.
NOW THE TOTAL TIME FOR THE BATSMAN TO ROW FROM X TO Z IS 4 HOURS. THEREFORE, TIME TO ROW FROM X TO Y IS 2 HOURS.
ALSO THE TIME FOR THE BOATS MAN TO ROW FROM X TO Y AND BACK IS 10 HOURS. HENCE, TIME REQUIRED TO ROW FROM Y TO X IS 8 HOURS.
IF, A: SPEED OF BOATS MAN IN STILL WATER
B: SPEED OF THE RIVER
D/(A + B) = 2; D/(A – B) = 8
2*(A + B) = 8*(A – B)
A + B = 4A – 4B
3A = 5B
A:B = 5:3
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X ———— Y ———— Z
IF ‘D’ IS THE DISTANCE BETWEEN X AND Y, THEN ‘D’ IS THE DISTANCE BETWEEN Y AND Z.
NOW THE TOTAL TIME FOR THE BATSMAN TO ROW FROM X TO Z IS 4 HOURS. THEREFORE, TIME TO ROW FROM X TO Y IS 2 HOURS.
ALSO THE TIME FOR THE BOATS MAN TO ROW FROM X TO Y AND BACK IS 10 HOURS. HENCE, TIME REQUIRED TO ROW FROM Y TO X IS 8 HOURS.
IF, A: SPEED OF BOATS MAN IN STILL WATER
B: SPEED OF THE RIVER
D/(A + B) = 2; D/(A – B) = 8
2*(A + B) = 8*(A – B)
A + B = 4A – 4B
3A = 5B
A:B = 5:3
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