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Time taken by a boat in going upstream a certain distance is twice the time taken in going the same distance downstream. Find the speed of boat upstream if it covers 20 km downstream in 1 hour 40 minutes.
A) 6 kmph
B) 7 kmph
C) 6.5 kmph
D) 7.2 kmph
Correct answer:
A) 6 kmph
Description for Correct answer:
Speed of boat in still water = x kmph.
Speed of current = y kmph.
Rate downstream = (x + y) kmph
Rate upstream = (x - y) kmph,
According to the question,
\( \Large x + y = \frac{20}{1 \frac{40}{60}} \) kmph
=> \( \Large x + y = \frac{20}{\frac{5}{3}} = \frac{20 \times 3}{5} \)
= 12 kmph ....(i)
\( \Large \therefore \frac{2 \times 20}{x + y} = \frac{20}{x - y} \)
=> 2x - 2y = x + y
=> x = 3y ....(ii)
From equation (i),
3y + y = 12
=> \( \Large 4y = 12 => y = \frac{12}{4} = 3 \ kmph \)
\( \Large \therefore x = 3 \times 3 = 9 \ kmph \)
\( \Large \therefore \) Rate upstream
= (x - y) kmph
= 9 - 3 = 6 kmph
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