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 replaced is:
By the rule of alligation, we have:
Strength of first jar = 40%
Strength of 2nd jar = 19%
Main Strength = 26%
So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2
So, Required quantity replaced = \(\frac{2}{3}\)
To solve this problem, let us first define some variables.
Let’s say,
Q = Quantity of whisky in the jar
%A = Percentage of alcohol in the jar
%B = Percentage of alcohol in the whisky replaced
We are given the following information:
Q = 1
%A = 40 %
%B = 19 %
Now, the task is to find the quantity of whisky replaced.
Now, using the formula for finding the percentage, we can write:
%A = (Quantity of whisky with 40% alcohol/Total Quantity of whisky)*100
%B = (Quantity of whisky with 19% alcohol/Total Quantity of whisky)*100
From the given information, we can write:
40% = (Q/Q)*100
19% = (Q2/Q)*100
Where Q2 is the quantity of whisky replaced with 19% alcohol.
Now, we need to find the value of Q2.
To do this, let us rearrange the equation to get:
Q2 = (19/40)*Q
Now, we need to find the value of Q.
To do this, let us rearrange the equation to get:
Q = (40/19)*Q2
Substituting the value of Q2 in the equation, we get:
Q = (40/19)*(19/40)*Q
Simplifying the equation, we get:
Q = (40/19)*Q
Dividing both the sides by Q, we get:
(40/19)*Q/Q = 1
Simplifying the equation, we get:
40/19 = 1
Now, we need to find the value of Q2.
Substituting the value of Q in the equation, we get:
Q2 = (19/40)*(40/19)*Q
Simplifying the equation, we get:
Q2 = Q
Therefore, the quantity of whisky replaced is equal to the total quantity of whisky in the jar.
Hence, the answer is Option B 2/3
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