Concept: The question tests on Mixtures and Alligation
It can be seen clearly that this is a problem on mixtures. Whenever you come across a question on mixtures (or on weighted averages for that matter), use the Alligation diagram to solve the question in a quick and efficient way.
We have two solutions with us:
x litres of milk that contains 10% water by weight.
y litres of milk that contains 2 % water by weight.
We mix the above solutions to obtain a new mixture z that has 5% water by weight.
The percentage of water in each milk solution, is the quality that we have to consider while drawing the Alligation diagram. Drawing the alligation diagram, we obtain one that is as follows:
From the alligation diagram, we understand that we need to mix the solutions x and y in the ratio of 3:5 to obtain the mixture z which has 5% water by weight.
That is, if we mix 3k litres of solution x with 5k litres of solution y, we obtain 8k litres of solution z (which has 5% water by weight).
The question asks us to find the value of x i.e. 3k. Any information that can give us ‘k’ will be sufficient information.
From statement I alone, y = 12. This means, 5k = 12 or k = 12/5 = 2.4. Since we know k = 2.4, we can find out x = 3k = 7.2.
Statement I alone is sufficient to find the value of x. Answer options B, C and E can be eliminated. Possible answer options are A or D.
From statement II alone, z = 20. This means 8k = 20 or k = 20/8 = 5/2= 2.5. Since we know k, we can find out x = 3k = 7.5.
Statement II alone is sufficient to find the value of x. Answer option A can be eliminated.
The correct answer option is D.