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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:

Options:
A .  \(\frac{1}{3}\)
B .  \(\frac{2}{3}\)
C .  \(\frac{2}{5}\)
D .  \(\frac{3}{5}\)
Answer: Option B

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.
Lets 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

If you think the solution is wrong then please provide your own solution below in the comments section .


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