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The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed

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Math Expert
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Joined: 02 Sep 2009
Posts: 58427
The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed  [#permalink]

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New post 29 Jan 2019, 06:11
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (02:58) correct 40% (02:48) wrong based on 94 sessions

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Joined: 18 Aug 2017
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Concentration: Sustainability, Marketing
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Re: The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed  [#permalink]

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New post 29 Jan 2019, 06:23
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1
Bunuel wrote:
The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed in the ratio 1:4. The resulting mixture will have water and milk in the ratio.

(A) 31:74
(B) 31:75
(C) 30:77
(D) 30:74
(E) 31:77



Quantity of water in the resultant mixture
1*1/3 + 4*2/7 = 1/3 + 8/7 = 31/21

Quantity of milk in the resultant mixture
1*2/3 + 4*5/7 = 2/3 + 20/7 = 74/21

Required ratio
31/21 : 74/21
= 31 : 74
IMO A
General Discussion
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Re: The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed  [#permalink]

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New post 14 Oct 2019, 10:09
I need details,, why cant sole by using allegation method.

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Re: The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed  [#permalink]

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New post 16 Oct 2019, 00:30
Hi,

Here is the alligation diagram that can be used while solving questions like this. You need to keep two things in mind while using this:

1. The higher value (HV), the lower value (LV) and the mean value (MV) have to be all values that are associated to the word per (for example: percents, averages, costs)
2. You select a quantity that overlaps between the higher, lower and mean values.

Attachment:
File comment: The Alligation Diagram
Capture.PNG
Capture.PNG [ 144.4 KiB | Viewed 295 times ]


Now here the question gives us two solutions of milk and water,

Solution 1 - W : M -----> 1 : 2 -----> W = 1/3 and M = 2/3

Solution 2 - W : M -----> 2 : 5 -----> W = 2/7 and M = 5/7

Now we need to mix these two in the ratio of 1 : 4, so we have been given HV - MV : MV - LV = 1 : 4

Drawing the mixture diagram for solution 1

Attachment:
Capture 1.PNG
Capture 1.PNG [ 94.97 KiB | Viewed 293 times ]


Drawing the mixture diagram for solution 2

Attachment:
Capture 2.PNG
Capture 2.PNG [ 98.35 KiB | Viewed 292 times ]


Combining these two ratios we get

Attachment:
Capture 3.PNG
Capture 3.PNG [ 77.34 KiB | Viewed 290 times ]
GMAT Club Bot
Re: The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed   [#permalink] 16 Oct 2019, 00:30
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The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed

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