Alligations or Mixtures
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Q.

From a cask of milk containing 30 litres, 6 litres are drawn out and the cask is filled up with water.

If the same process is repeated a second, then a third time, what will be the number of litres of milk left in the cask?

 A.

5.12 litres

 B.

12 litres

 C.

14.38 litres

 D.

15.36 litres

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Solution:
Option(D) is correct

The problem can be solved by traditional method but it is a cumbersome process to do that. The problem is simple if its solution is simpler. Hence, we will go for a simpler solution for this kind of problem. 

There is a shortcut method to find the Quantity of milk left after $n^{th}$ operation

It is given by $\left(\dfrac{x-y}{x}\right)^n$ of the whole quantity, where $x$ is the initial quantity of milk in the cask $y$ is the quantity of milk withdrawn in each process and $n$ is the number of processes.

Hence from the above rule it can be say that, 

Quantity of milk left after the 3rd operation $=30\times \left(\dfrac{30-6}{30}\right)^n$
$=15.36$ litres.

Edit:  To know more about the formula used in the solution, check the introduction section.


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