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.
Answer: B