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A container is completely filled with a sugar solution composed of wat

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Bunuel
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A container is completely filled with a sugar solution composed of wat [#permalink] New post   03 Jun 2020, 10:57
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A container is completely filled with a sugar solution composed of water and sugar syrup in the ratio of 7:3. The container has 2 holes covered with filters such that from one of the holes only sugar syrup can flow out and from the other hole only water can flow out. The rates of water outflow and sugar syrup outflow from their respective holes are x cubic centimeters per hour and y cubic centimeters per half an hour respectively, such that x:y = 5:1. If the water from the solution can be drained out completely in 14 hours from the hole, how much time in hours would it take the container to be empty if both the holes are opened simultaneously?

A. 14
B. 15
C. 29
D. 30
E. 44


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yashikaaggarwal
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A container is completely filled with a sugar solution composed of wat [#permalink] New post   Updated on: 07 Jun 2020, 11:06
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Let the container contain 100 litre of sugar solution.
Out of which 70 is water and 30 is sugar syrup
The pipe x drains 5z in an hour.
Draining 70 litre is 70/5z in 14/z hour
Since pipe x drain complete water in 14 hours. 14/z=14
Z=1

Z litre is drained out of pipe y in half an hour.
2Z in an Hour
30 litre will be drained in 30/2z => 15 hours.

Answer should be B

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Originally posted by yashikaaggarwal on 03 Jun 2020, 12:21.
Last edited by yashikaaggarwal on 07 Jun 2020, 11:06, edited 1 time in total.
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Re: A container is completely filled with a sugar solution composed of wat [#permalink] New post   07 Jun 2020, 11:07
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Lipun Babineaux Guys we have been wrongly interpreting whole passage. The sugar syrup is been drained out at the rate of x per half an hour. That means 2x in an hour. And 30 will be emptied in 15 hours.

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Re: A container is completely filled with a sugar solution composed of wat [#permalink] New post   08 Jun 2020, 13:53
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Bunuel wrote:
A container is completely filled with a sugar solution composed of water and sugar syrup in the ratio of 7:3. The container has 2 holes covered with filters such that from one of the holes only sugar syrup can flow out and from the other hole only water can flow out. The rates of water outflow and sugar syrup outflow from their respective holes are x cubic centimeters per hour and y cubic centimeters per half an hour respectively, such that x:y = 5:1. If the water from the solution can be drained out completely in 14 hours from the hole, how much time in hours would it take the container to be empty if both the holes are opened simultaneously?

A. 14
B. 15
C. 29
D. 30
E. 44




Solution:

We can let the amount of water in the solution be 70 cm^3 and the amount of sugar syrup in the solution be 30 cm^3. We can also let x = 5 and thus y = 1 (notice that this takes exactly 70/5 = 14 hours to drain the water completely). Since it takes y = 1 cm^3 per half an hour to drain the syrup, the rate of draining the syrup is 2 cm^3 per hour. Since there are 30 cm^3 of syrup, it will take 30/2 = 15 hours to drain the syrup completely. Finally, since both the holes are opened simultaneously, it takes the larger of the two times (14 hours and 15 hours) to empty the solution in the container. Therefore, it takes 15 hours to empty the solution in the container.

Answer: B
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A container is completely filled with a sugar solution composed of wat [#permalink] New post   Updated on: 07 Jun 2020, 19:48
W:S = 7:3 => S = 3*W/7
x:y = 5:1 => y = x/5

x cc/hr implies in 14 hrs, it will drain 14x cc of water. So, S = 3*14x/7 = 6x
2x/5 of S is drained out every hour, so 6x will be drained out in 15 hrs.

Ans: 15

Originally posted by Lipun on 03 Jun 2020, 21:44.
Last edited by Lipun on 07 Jun 2020, 19:48, edited 1 time in total.
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Re: A container is completely filled with a sugar solution composed of wat [#permalink] New post   04 Jun 2020, 15:33
i vote for B

14 hours it takes to empty 7 so it takes 1/2 hour to empty 1 L of water.

1/2 is in a ratio of 5:2 to sugaer (as water is per hour and suger per 1/2 hour) so sugaer is 1/5 K per hour (as 5/10 to 2/10 is 5:2).

so x hours*1/5 should equal 3. hence x=15

so the water will be emptied after 14 hours and sugar 1 hour afterwards. so 15
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Re: A container is completely filled with a sugar solution composed of wat [#permalink] New post   06 Jun 2020, 16:58
If 100L syrup is assumed
Then 70L is water and 30L is sugar
Now flowrate of water is 5 L/hr (14hrs for complete water)
If S hrs is required for complete sugar then flowrate of sugar will be S/30 L/hr
Given ratio of flowrates is 5:1
Therefore calculating we can obtain S= 30 hrs
If both the holes are kept open simultaneously then at 14 hrs water will come out completely
And after 30 hrs sugar will be filtered
Thus overall 30 hrs will take to complete the process.

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Re: A container is completely filled with a sugar solution composed of wat [#permalink] New post   07 Jun 2020, 11:51
yashikaaggarwal wrote:
Lipun Babineaux Guys we have been wrongly interpreting whole passage. The sugar syrup is been drained out at the rate of x per half an hour. That means 2x in an hour. And 30 will be emptied in 15 hours.

Posted from my mobile device



Oh My God, I wrongly interpreted.
Sorry, yes its 15 hrs then.
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Re: A container is completely filled with a sugar solution composed of wat [#permalink]
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