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A motorboat whose speed is 20 Kmph in still water goes 30 km downstrea
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29 May 2021, 04:16
29 May 2021, 04:16
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Question Stats:
59% (01:53) correct
40% (01:45) wrong based on 27 sessions
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A motorboat whose speed is 20 Kmph in still water, goes 30 km downstream and comes back in 5 hours.
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Speed of the stream |
10 |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: A motorboat whose speed is 20 Kmph in still water goes 30 km downstrea
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30 May 2021, 06:21
30 May 2021, 06:21
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Time = \(\frac{Distance}{Speed}\)
5 = \(\frac{Total Distance travelled}{Speed in still water + Speed in stream}\) + \(\frac{Total Distance travelled}{Speed in still water - Speed in stream}\)
Let the speed in stream be X kmph
5 = \(\frac{30}{20+x}\) +\(\frac{30}{20-x }\)
On Solving, We get
400 -\(x^2\)= 240
\(x^2\) = 160
Taking Square root, it will be approx 4*3.16 which is greater than 10.
Hence A
5 = \(\frac{Total Distance travelled}{Speed in still water + Speed in stream}\) + \(\frac{Total Distance travelled}{Speed in still water - Speed in stream}\)
Let the speed in stream be X kmph
5 = \(\frac{30}{20+x}\) +\(\frac{30}{20-x }\)
On Solving, We get
400 -\(x^2\)= 240
\(x^2\) = 160
Taking Square root, it will be approx 4*3.16 which is greater than 10.
Hence A
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A motorboat whose speed is 20 Kmph in still water goes 30 km downstrea
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18 Jun 2021, 11:23
18 Jun 2021, 11:23
1
Theory
Downstream: If a boat with speed v in still water is going down on a stream of water which is flowing at speed u then the speed of the boat downstream will become v + u
Upstream: If a boat with speed v in still water is going up on a stream of water which is flowing at speed u then the speed of the boat Upstream will become v - u
Let Speed of the stream is u kmph
Downstream
Distance = 30 km
Speed = 20 + u kmph
Time = \(\frac{Distance}{Speed}\) = \(\frac{30 km}{20+u kmph}\)
= \(\frac{30 }{ 20+u}\) hours
Upstream
Distance = 30 km
Speed = 20 - u kmph
Time = \(\frac{Distance}{Speed}\) = \(\frac{30 km}{20-u kmph}\)
= \(\frac{30 }{ 20-u}\) hours
Total Time Downstream + Upstream = \(\frac{30 }{ 20+u}\) hours + \(\frac{30 }{ 20-u}\) hours = 5 hours [given]
=> 30*(20-u) + 30*(20+u) = 5*(20-u)*(20+u) [ Divide both sides by 5 we get]
=> 6*(20-u) + 6*(20+u) = \(20^2\) - \(u^2\) [ Using (a-b)*(a+b) = \(a^2\) - \(b^2\) ]
=> 120 - 6u + 120 + 6u = 400 - \(u^2\)
=> 240 = 400 - \(u^2\)
=> \(u^2\) = 400 - 240 = 160
=> u = 12.64
=> Quantity A (12.64) > Quantity B (10)
So, answer will be A
Hope it helps!
Downstream: If a boat with speed v in still water is going down on a stream of water which is flowing at speed u then the speed of the boat downstream will become v + u
Upstream: If a boat with speed v in still water is going up on a stream of water which is flowing at speed u then the speed of the boat Upstream will become v - u
Let Speed of the stream is u kmph
Downstream
Distance = 30 km
Speed = 20 + u kmph
Time = \(\frac{Distance}{Speed}\) = \(\frac{30 km}{20+u kmph}\)
= \(\frac{30 }{ 20+u}\) hours
Upstream
Distance = 30 km
Speed = 20 - u kmph
Time = \(\frac{Distance}{Speed}\) = \(\frac{30 km}{20-u kmph}\)
= \(\frac{30 }{ 20-u}\) hours
Total Time Downstream + Upstream = \(\frac{30 }{ 20+u}\) hours + \(\frac{30 }{ 20-u}\) hours = 5 hours [given]
=> 30*(20-u) + 30*(20+u) = 5*(20-u)*(20+u) [ Divide both sides by 5 we get]
=> 6*(20-u) + 6*(20+u) = \(20^2\) - \(u^2\) [ Using (a-b)*(a+b) = \(a^2\) - \(b^2\) ]
=> 120 - 6u + 120 + 6u = 400 - \(u^2\)
=> 240 = 400 - \(u^2\)
=> \(u^2\) = 400 - 240 = 160
=> u = 12.64
=> Quantity A (12.64) > Quantity B (10)
So, answer will be A
Hope it helps!
