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Two vessels having volumes in the ratio 3:5 are filled with

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Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 18 Sep 2013, 07:48
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Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160
[Reveal] Spoiler: OA
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Re: Two vessels having volumes in the ratio 3:5 are filled [#permalink] New post 18 Sep 2013, 07:55
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abid1986 wrote:
Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160


Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;

Vessel A + B = 800 gallons --> milk = 495, water 305.

The ratio = 495/305 --> reduce by 5 = 99/61.

Answer: A.
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Re: Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 18 Sep 2013, 08:42
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I solved this by drawing two canisters with the milk/water proportions and then set them equal (2:3 becomes 6:9 and 3:1 becomes 6:2). Once we draw the final (biggest) canister we can see that the proportion of milk (6+6=12) is larger than the proportion of water (2+9=11) and the answer "A"is the only one that gives us this choice :)
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Re: Two vessels having volumes in the ratio 3:5 are filled [#permalink] New post 19 Sep 2013, 17:19
Can you explain how you quickly arrived at 300 : 500 gallons?

I understand that A needs to be a multiple of 5, and B of 4, but I'm not quite sure how to find good values to use in a time efficient manner. I started at 15 and 25, then went up, and it took me too long...

Thanks

Bunuel wrote:
abid1986 wrote:
Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160


Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;

Vessel A + B = 800 gallons --> milk = 495, water 305.

The ratio = 495/305 --> reduce by 5 = 99/61.

Answer: A.
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Re: Two vessels having volumes in the ratio 3:5 are filled [#permalink] New post 20 Sep 2013, 01:05
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grant1377 wrote:
Can you explain how you quickly arrived at 300 : 500 gallons?

I understand that A needs to be a multiple of 5, and B of 4, but I'm not quite sure how to find good values to use in a time efficient manner. I started at 15 and 25, then went up, and it took me too long...

Thanks

Bunuel wrote:
abid1986 wrote:
Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160


Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;

Vessel A + B = 800 gallons --> milk = 495, water 305.

The ratio = 495/305 --> reduce by 5 = 99/61.

Answer: A.


I chose big numbers in the ratio 3 to 5. So, that A is also a multiple of 5 and B is also a multiple of 4 (since the ratio of milk and water in the two vessels are 2:3 (5 parts) and 3:1 (4 parts) respectively, then A should be a multiple of 5 and B should be a multiple of 4).
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Re: Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 21 Sep 2013, 20:42
let volume of first vessel is 3 and second vessel is 5.

total volume of milk = 3(2/5)+5(3/4) = 99/20
total volume of water= 3(3/5)+5(1/4) = 61/20

Milk : water = 99:61
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Re: Two vessels having volumes in the ratio 3:5 are filled [#permalink] New post 24 Sep 2013, 01:58
Expert's post
grant1377 wrote:
Can you explain how you quickly arrived at 300 : 500 gallons?

I understand that A needs to be a multiple of 5, and B of 4, but I'm not quite sure how to find good values to use in a time efficient manner. I started at 15 and 25, then went up, and it took me too long...

Thanks

Bunuel wrote:
abid1986 wrote:
Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160


Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;

Vessel A + B = 800 gallons --> milk = 495, water 305.

The ratio = 495/305 --> reduce by 5 = 99/61.

Answer: A.


A few pointers when assuming numbers:
Try to stick to multiples of 10 or 100 as the case may be.
Given 3:5, I would first look at 30 and 50 or 300 and 500. I would not look at 15 and 25 because when I am assuming value, nothing says they need to be as small as possible. Answer won't change even if they are a little larger but with multiples of 10, my calculations may be much simpler.
Next, I need first one to be a multiple of 5 and the next one to be a multiple of 4. 30 and 50 will not satisfy but 300 and 500 will.
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Re: Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 06 Oct 2013, 02:24
@karishma:

I think we can always multiply the two total parts of the proportions, i.e 2:3 =5 parts and 3:1 = 4 parts and 5*4=20

then follow the process that bunuel explained.
???
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Re: Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 06 Oct 2013, 19:30
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sayansarkar wrote:
@karishma:

I think we can always multiply the two total parts of the proportions, i.e 2:3 =5 parts and 3:1 = 4 parts and 5*4=20

then follow the process that bunuel explained.
???


I am not sure what you mean. Do you mean to say that we can take the volume of vessel A as 20 gallons? or do you mean that we can take the volume of vessel A as 20*3 gallons?

Note that either case will be correct because when you are assuming numbers, you will get the correct answer for every correct set of numbers you take. The point is of convenience.
If vessel A has volume of 20 gallons, the volume of vessel B will not be a whole number.

Vessel A = 20 gallons --> milk = 8, water = 12;
Vessel B = 100/3 gallons --- complications

If volume of vessel A is taken as 20*3 = 60 gallons, then it is fine.
Vessel A = 20*3 gallons = 60 gallons --> milk = 24, water = 36;
Vessel B = 20*5 gallons = 100 gallons --> milk = 75, water = 25;

Total milk:water = (24+75):(36+25) = 99:61
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Re: Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 26 Nov 2013, 01:35
Dear Karishma,
Please help explain how we can use your scale method to solve this question.
Here'e up to where i got.

2/5 3/8 ¾
31/40 9/8

Then I flipped the two ratios so its 9/8 to 31/40
Then I got stuck.

Ps. Sorry the lines wouldn't appear
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Re: Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 27 Nov 2013, 19:45
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mumbijoh wrote:
Dear Karishma,
Please help explain how we can use your scale method to solve this question.
Here'e up to where i got.

2/5 3/8 ¾
31/40 9/8

Then I flipped the two ratios so its 9/8 to 31/40
Then I got stuck.

Ps. Sorry the lines wouldn't appear


According to scale method:

w1/w2 = (C2 - Cavg)/(Cavg - C1)

3/5 = (3/4 - Cavg)/(Cavg - 2/5) (Working with only milk here. Note that concentration of milk is 3/4 in second vessel since milk:water is 3:1. Also, the ratio of the volume of two solutions that are mixed is 3:5. It is not the concentration of milk in the final solution. So w1/w2 = 3/5)

8/5Cavg = 3/4 + 6/25
Cavg = 99/160

Milk:Water in final solution = 99:61
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Re: Two vessels having volumes in the ratio 3:5 are filled with [#permalink] New post 28 Nov 2013, 07:21
Karishma,
Your totally right.I must have misread that question.Thanks a lot for the clarification!
Re: Two vessels having volumes in the ratio 3:5 are filled with   [#permalink] 28 Nov 2013, 07:21
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