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# A jar full of whisky contains 40% alcohol. A part of this whisky is re

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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
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anceer wrote:
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?

A. 1/3
B. 2/3
C. 2/5
D. 3/5
E. 4/5

another approach to the Q..

the ratio of alcohol in two mix are 40 and 19 and the final is 26..

By the weighted average method
Qty of 19% in final mix= (40-26)/(40-19)=14/21=2/3..
Initially there was nothing and 19% has come by replacement, so 2.3 of initial qty has been replaced
ans 2/3....B
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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
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let x=quantity of whiskey replaced
.4-.4x+.19x=.26
x=2/3
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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
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0.40x+0.19(1-x)=0.26
0.21x=0.07
x=7/21 =1/3

B = 1-x = 1-(1/3) = 2/3

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A jar full of whisky [#permalink]
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A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing
19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of
whisky replace is:

a) 1/3
b) 2/3
c) 2/5
d) 3/5
e) 1/5
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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
daboo343 wrote:
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing
19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of
whisky replace is:

a) 1/3
b) 2/3
c) 2/5
d) 3/5
e) 1/5

Merging topics. Please refer to the discussion above.
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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
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VeritasPrepKarishma wrote:
anceer wrote:

40% alcohol solution is mixed with 19% alcohol solution to give 26% alcohol solution.

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 26)/(26 - 19) = 14/7 = 2/1
So 2 parts of 19% solution were mixed with 1 part of 40% solution. This means that 2/3rd of the 40% solution was replaced by 19% solution.

I am unable to grasp the concept behind it. We found that 2 parts of 19% solution mixed with 1 part of 40% solution. But how does that lead to the replacement of 2/3rd?
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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
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TheMastermind wrote:
VeritasPrepKarishma wrote:
anceer wrote:

40% alcohol solution is mixed with 19% alcohol solution to give 26% alcohol solution.

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 26)/(26 - 19) = 14/7 = 2/1
So 2 parts of 19% solution were mixed with 1 part of 40% solution. This means that 2/3rd of the 40% solution was replaced by 19% solution.

I am unable to grasp the concept behind it. We found that 2 parts of 19% solution mixed with 1 part of 40% solution. But how does that lead to the replacement of 2/3rd?

We see that to get 26% alcohol, we have mixed 2 parts 19% alcohol with 1 part 40% alcohol. But initially it was all 40% alcohol. We removed some of it and put 19% alcohol in its place. How much did we remove? We see that if we split the initial total into 3 parts, we removed 2 parts and put 19% alcohol in its place. We still have 1 part of the 40% alcohol. These two mixed together to give us 26% alcohol.
Hence, 2/3rd of the 40% alcohol was replaced.
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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
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anceer wrote:
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?

A. 1/3
B. 2/3
C. 2/5
D. 3/5
E. 4/5

We can let x = the amount of whisky containing 40% alcohol and y = the amount of whisky containing 19% alcohol. Thus, the amount of alcohol in the 40%-alcohol whisky is 0.4x and the amount of alcohol in the 19%-alcohol whisky is 0.19y. Furthermore, the amount of 40%-alcohol whisky being replaced from the jar is y and the amount of alcohol being replaced from the jar is 0.4y.

Thus, the amount of alcohol in the jar after the y amount of whisky has been replaced is 0.4x - 0.4y + 0.19y. However, the amount of whisky in the jar is still x after the y amount of whisky has been replaced, since x - y + y = x.

Thus, after y amount of whisky has been replaced, we have:

(0.4x - 0.4y + 0.19y)/x = 0.26

0.4x - 0.21y = 0.26x

0.14x = 0.21y

14x = 21y

y = 14x/21

y = 2x/3 = (⅔)x

Thus, ⅔ of the amount of whisky is replaced.

Alternate Solution:

Let’s assume the jar has x liters to start with. We start with x liters of whisky with 0.40 alcohol. We take out y liters of (the original) whisky with 0.40 alcohol and replace it with y liters of whisky with 0.19 alcohol. The result is that we have x liters of whisky with 0.26 alcohol. We can summarize these actions with the following equation:

0.40x – 0.40y + 0.19y = 0.26x

0.40x -0.21y = 0.26x

0.14x = 0.21y

14x = 21y

2x = 3y

(2/3)x = y

Since y was the amount replaced, we see that we replaced 2/3 of the original whisky.

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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
To solve this one I used the Alligation method explained here: https://gmatclub.com/forum/tips-and-tric ... 51906.html

Check it out! It's very useful for mixture questions!
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Re: A jar full of whisky contains 40% alcohol. A part of this whisky is re [#permalink]
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