Question

A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

Answer 1

Hint: First consider process 1, then subtract the amount of milk to be taken and add it to water instead. Now at the end of the first step, calculate the ratio of milk to water in the container. Then in the second step, the amount of milk taken out will be in proportion to how much it was presently there and use the same work. Now, repeat the process for last time and get the result.

Complete step-by-step answer:
It is given in the question that a container contains 40 litres of milk. Then, it is said that 4 litres of milk was taken out and replaced by water. This process was repeated two more times which means that a total of three times the process was done. Now, after the third time, we have to find out how much milk is remaining in the container. So, let us find the amount of milk remaining step by step, so after every process we will find out the milk to water ratio.
After the first process, that is after replacing 4 litres of milk with 4 litres of water, we get (40 - 4) = 36 litres of milk and 4 litres of water in the container. So, the milk to water ratio is 36:4 that is 9:1.
For the second process, we have a mixture of milk and water, so we will take out 4 litres of the mixture which has the ratio 9:1, that is it has 9 parts of milk and 1 part of water. So, 4 litres of the mixture contains 3.6 litres of milk and 0.4 litres of water. So, after taking the mixture out and replacing it with 4 litres of water, the remaining amount of milk is (36 – 3.6) = 32.4 litres and the amount of water is (3.6 + 4) = 7.6 litres. So, the milk to water ratio is 32.4:7.6 in the container.
Now for the third process, 4 litres of the mixture is taken out which has the ratio 32.4:7.6, so it contains 3.24 litres of milk and 0.76 litres of water. So, after taking the mixture out and adding 4 litres of water, the amount of milk = (32.4 – 3.24) = 29.16 litres.
Therefore, we get the amount of milk remaining in the container as 29.16 litres.

Note: The volume of milk remaining after the three processes can also be found out using the formula,
$V=N{{\left( 1-\dfrac{P}{N} \right)}^{n}}$, where N is the original amount of milk, n is the number of processes and P is the amount of milk taken for each process.