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

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

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

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.

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.

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.

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

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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