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Difficulty:
95%
(hard)
Question Stats:
40% (03:08) correct
60%
(03:23)
wrong
based on 50
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The total time taken by a boat to travel \(x\) km downstream and \((x - 5)\) km upstream was 569.2 minutes. If the difference between the speed of the boat downstream and that in upstream is 3 kmph and the respective ratio between speed of boat in still water and speed of water current was (9 : 1), what is the value of x?
A) 63.8
B) 34.4
C) 29.4
D) 68.8
E) 62.5
A) 63.8
B) 34.4
C) 29.4
D) 68.8
E) 62.5
I'm getting 66.02 but correct answer is marked as 68.8
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Updated on: 15 Jun 2018, 09:47
Originally posted by WizakoBaskar on 15 Jun 2018, 09:10.
Last edited by WizakoBaskar on 15 Jun 2018, 09:47, edited 1 time in total.
Last edited by WizakoBaskar on 15 Jun 2018, 09:47, edited 1 time in total.
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pv8172
Let the speed of the boat in still water be B km/hr
Let the speed of water current be S km/hr.
Downstream speed = B + S
Upstream speed = B - S
Given data 1: Difference between speed of boat downstream and that upstream = 3 km/hr
So, (B + S) - (B - S) = 3
Or 2S = 3 or S = 1.5 km/hr.
Given data 2: Ratio between speed of boat in still water and speed of water current was (9 : 1)
B : S = 9 : 1
If S = 1.5 km/hr, B = 9*1.5 = 13.5 km/hr
The boat travels x km downstream. i.e., the boat travels x km @ (13.5 + 1.5) = 15 km/hr
The boat travel (x - 5) km upstream. i.e., the boat travels (x - 5)km @ (13.5 - 1.5) = 12 km/hr
Given data 3: Total time taken = 569.2 minutes = \(\frac{569.2}{60}\) hours.
Total time taken = \(\frac{x}{15} + \frac{{x - 5}}{12} = \frac{569.2}{60}\)
\(\frac{{4x + 5x - 25}}{60} = \frac{569.2}{60}\)
\(\frac{{9x - 25}}{60} = \frac{569.2}{60}\)
or 9x - 25 = 569.2
So, 9x = 594.2
x = 66.02
None of the answer choices match. Could you please check the answer options?
15 Jun 2018, 09:29
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WizakoBaskar
You are wrong in highlighted portion..
\(\frac{{4x + 5x - 75}}{60} = \frac{569.2}{60}\)
It will be 4x+5x-25
