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A mixture consists of two spirits A and B; A evaporates at the rate of

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A mixture consists of two spirits A and B; A evaporates at the rate of [#permalink]

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A mixture consists of two spirits A and B; A evaporates at the rate of 2 ml per minute and B at 3 ml per minute. What will be the volume of the mixture after 10 minutes?

(1) Initial ratio of A and B in the mixture was 4 : 5.
(2) The final ratio of A and B in the mixture was 5 : 4.
[Reveal] Spoiler: OA

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Re: A mixture consists of two spirits A and B; A evaporates at the rate of [#permalink]

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New post 05 Jul 2017, 01:03
Bunuel wrote:
A mixture consists of two spirits A and B; A evaporates at the rate of 2 ml per minute and B at 3 ml per minute. What will be the volume of the mixture after 10 minutes?

(1) Initial ratio of A and B in the mixture was 4 : 5.
(2) The final ratio of A and B in the mixture was 5 : 4.


(1) gives us the initial ratio before evaporation happened

now in 10 mins A evaporated 20 ml and b evaporated 30 ml

if the initial ratio was 4/5 lets say the total volume was 9x and A:B was 4x:5x

Pre Evaporation
A : B ::: Total Volume
4x:5x ::: 9x
Post evaporation
A : B ::: Total Volume
4x-20:5x-30 ::: 9x-50
But we dont know the value of x hence Not sufficient

(2) gives us Post evaporation ratio
A : B ::: Total Volume
5y : 4y ::: 9y

Pre evaporation it was
A : B ::: Total Volume
5y+20 : 4y +30 ::: 9y+50

But we dont know the value of y hence Not sufficient

On combining both we can solve
4x-20/9x-50 = 4y/9y
we can solve to get the value of x

Hence Sufficient C
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Re: A mixture consists of two spirits A and B; A evaporates at the rate of [#permalink]

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New post 21 Aug 2017, 00:21
Bunuel wrote:
A mixture consists of two spirits A and B; A evaporates at the rate of 2 ml per minute and B at 3 ml per minute. What will be the volume of the mixture after 10 minutes?

(1) Initial ratio of A and B in the mixture was 4 : 5.
(2) The final ratio of A and B in the mixture was 5 : 4.


Hi Bunuel

I am trying to solve this question using the allegation method. But I am messing up somewhere. Can you please explain how to solve it using the w1/w2=(A2-Aavg)/(Aavg-A1) (weighted average) method?

Thank you
Dkingdom

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Re: A mixture consists of two spirits A and B; A evaporates at the rate of [#permalink]

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New post 21 Aug 2017, 00:54
We don't know the initial volume so how can we get the final volume?
Please explain, thank you

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Re: A mixture consists of two spirits A and B; A evaporates at the rate of [#permalink]

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New post 21 Aug 2017, 01:18
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pclawong wrote:
We don't know the initial volume so how can we get the final volume?
Please explain, thank you


Hi pclawong
we do not know the initial volume hence assumed it to be 9x
throuugh pre-evaporation we have two equations from (1) and (2)
4x-20 = 5y
5x-30 = 4y

4x-5y = 20
5x-4y = 30

20x - 25y = 100
20x - 16y = 120

9y = 20
y=20/9 and x= 70/9

hence pre-evaporation volume was 70 ml and post evaporation volume will be 20 ml
Let me know if it helped
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Re: A mixture consists of two spirits A and B; A evaporates at the rate of [#permalink]

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New post 21 Aug 2017, 03:35
pclawong wrote:
We don't know the initial volume so how can we get the final volume?
Please explain, thank you


Alternatively you can use the following method:
We can solve this problem by equating the amounts of either A or B before and after evaporation.
CiVi = CfVf

As per the question, 20ml of A and 30ml of B have evaporated.

Lets solve for A.

(1)
Ci=4/9
(4/9) * x = Cf * (x-20)
We need to find x (total volume after 10 mins)
Since we do not have the value of Cf we cannot solve for x.
Insufficient

(2)
Cf=5/9
Ci * x = (5/9) * (x-20)
We need to find x (total volume after 10 mins)
Since we do not have the value of Ci we cannot solve for x.
Insufficient

(1) + (2)
Ci=4/9, Cf=5/9
(4/9) *x = (5/9) * (x-20)

Now we can solve for x

Ans : C

Hope it helps.

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Re: A mixture consists of two spirits A and B; A evaporates at the rate of   [#permalink] 21 Aug 2017, 03:35
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