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A man can row 50 km upstream and 72 km downstream in 9 hours. He can

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Joined: 02 Sep 2009
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A man can row 50 km upstream and 72 km downstream in 9 hours. He can  [#permalink]

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New post 19 Jan 2020, 23:33
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Difficulty:

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Question Stats:

31% (03:20) correct 69% (02:30) wrong based on 13 sessions

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Re: A man can row 50 km upstream and 72 km downstream in 9 hours. He can  [#permalink]

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New post 20 Jan 2020, 00:25
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Question)
A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.


Solution:
Let the speed of the man and current be m and r km/hr respectively
Thus, we have:
Scenario 1: 50/(m-r) + 72/(m+r) = 9 ... (i)
Scenario 1: 70/(m-r) + 90/(m+r) = 12 ... (ii)

Assuming (m-r) = u and (m+r) = v and solving for u and v:
50/u + 72/v = 9
70/u + 90/v = 12

=> u = 10 and v = 18
=> m - r = 10 and m + r = 18

Solving: r = 4


Alternate method:

We know that:

70 km upstream (U) and 90 km downstream (D) takes 12 hours ... (i)

Also: 50 km upstream and 72 km downstream takes 9 hours
=> If we increase time by one-third its value, it would become 12 hours (as in first scenario); in that case, we need to increase the distances also by 1/3rd of the respective values
=> 200/3 km upstream (U) and 96 km downstream (D) takes 12 hours ... (ii)

Thus, equating the times from (i) and (ii):
200/3 (U) + 96 (D) = 70 (U) + 90 (D)
=> 10/3 (U) = 6 (D)
=> 10 (U) = 18 (D)
=> Time taken to cover 10 km upstream is the same as that taken to cover 18 km downstream

Let the speed of the man and current be m and r km/hr respectively

=> 10/(m-r) = 18/(m+r)
=> m : r = 7 : 2
=> m = 7k and r = 2k

Thus, from (i):
50/5k + 72/9k = 9
=> k = 2

=> Speed of the current = 2k = 4 km/hr

Answer C
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Re: A man can row 50 km upstream and 72 km downstream in 9 hours. He can   [#permalink] 20 Jan 2020, 00:25
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