A jar was full with Milk. A person used to draw out 33.33% of the Milk from the jar and replaced it with water. He has repeated the same process 4 times and thus there was only 96 ml of milk left in the jar, the rest part of the jar was filled with the water. The initial amount of milk in the jar was ______

Concept Used:-

In 2 liquid mixture of volume M, when first liquid with Initial amount (I) is replaced n times with quantity R of second, then the final amount of first liquid remain in the mixture is,

\(F=I\left(1-\frac{R}{M}\right)^n\)

Explanation:-

Given information;-

Number of times milk is replaced n = 4

Amount of milk replaced in 1 time R = 33.33%

Final amount of milk in jar F = 96 ml

Since, the whole jar was filled with milk. So, part of volume of milk in jar M = 1

Now, put the values in above formula to find the initial amount (I) of milk in jar,

\(\Rightarrow F=I\left(1-\frac{R}{M}\right)^n\)

\(\Rightarrow 96=I\left(1-\frac{(33.33/100)}{1}\right)^4\\ \Rightarrow 96=I\left(1-\frac{1}{3}\right)^4\\ \Rightarrow 96=I\left(\frac{3-1}{3}\right)^4\\ \Rightarrow 96=I\left(\frac{2}{3}\right)^4\\ \Rightarrow I=\frac{96\times3\times3\times3\times3}{2\times2\times2\times2}\\ \Rightarrow I=486 \rm \ \ ml\)

So, the initial amount of milk in the jar was 486 ml.

Hence, the correct option is 4.