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

Question

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

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

KarishmaB · Accepted Answer

These questions look like replacement questions but are actually just straight forward mixture problems with an added step.

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.

Answer (B)

ENGRTOMBA2018 · Answer

Do not forget to add the OA once you post a question.

Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.

Let x ml be the amount removed ---> total alcohol left = 4-0.4x

New quantity of whiskey added = x ml out of which 0.19 is the alcohol.

Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.

Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/3.

Hence, B is the correct answer.

Hope this helps.

chetan2u · Answer

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

gracie · Answer

let x=quantity of whiskey replaced
.4-.4x+.19x=.26
x=2/3

law258 · Answer

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

B is the correct answer.

daboo343 · Answer

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

Bunuel · Answer

Merging topics. Please refer to the discussion above.

profileusername · Answer

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?

KarishmaB · Answer

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.

JeffTargetTestPrep · Answer

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.
 
Answer: B

MvArrow · Answer

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!

bumpbot · Answer

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