Question: 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 ?
- 1/3
- 2/3
- 2/5
- 3/5
- 4/5
Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:
- A jar full of whisky contains 40% alcohol.
- A part of this whisky is replaced by another containing 19% alcohol
- Now the percentage of alcohol was found to be 26%.
Find out:
- The quantity of whisky was replaced.
It is said that 40% alcohol solution is mixed with 19% alcohol solution to give 26% alcohol solution.
Therefore, w1/w2 = (A2 - Aavg)/(Aavg - A1) = (40 - 26)/(26 - 19) = 14/7 = 2/1
Therefore, 2 parts of the 19% solution were mixed with 1 part of the 40% solution.
This implies that 2/3rd of the 40% solution was replaced by 19% solution.
Hence, the quantity of whisky replaced = 2/3.
Approach Solution 2:
The problem statement indicates that:
Given:
- A jar full of whisky contains 40% alcohol.
- A part of this whisky is replaced by another containing 19% alcohol
- Now the percentage of alcohol was found to be 26%.
Find out:
- The quantity of whisky was replaced.
Let’s assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed, then total alcohol remaining = 4 – 0.4x
A new quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Hence, the final quantity of alcohol = 4 – 0.4x + 0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.
According to the question, we need to find the x ml removed as a ratio of the initial volume.
Therefore, the ratio of initial volume= (20/3)/10 = 2/3.
Hence, the quantity of whisky replaced = 2/3.
Approach Solution 3:
The problem statement informs that:
Given:
- A jar full of whisky contains 40% alcohol.
- A part of this whisky is replaced by another containing 19% alcohol
- Now the percentage of alcohol was found to be 26%.
Find out:
- The quantity of whisky was replaced.
Let the amount of whisky containing 40% alcohol = x
Let the amount of whisky containing 19% alcohol = y
Thus, the amount of alcohol in the 40%-alcohol whisky is 0.4x
The amount of alcohol in the 19%-alcohol whisky is 0.19y.
Moreover, the amount of 40%-alcohol whisky being replaced from the jar is y.
The amount of alcohol being replaced from the jar is 0.4y.
Therefore, 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.
Hence, after y amount of whisky has been replaced, we get:
(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
Hence, the quantity of whisky replaced = 2/3.
“A jar full of whisky contains 40% alcohol”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The topic has been taken from the book “The Official Guide for GMAT Review 2017”. GMAT Problem Solving questions help the candidates to evaluate information and crack numerical problems. The GMAT Quant practice papers enable the candidates to practice different types of questions that will enhance their mathematical understanding.
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