Quantity of water in the resultant mixture
1*1/3 + 4*2/7 = 1/3 + 8/7 = 31/21

Quantity of milk in the resultant mixture
1*2/3 + 4*5/7 = 2/3 + 20/7 = 74/21

Required ratio
31/21 : 74/21
= 31 : 74
IMO A

Hi,

Here is the alligation diagram that can be used while solving questions like this. You need to keep two things in mind while using this:

1. The higher value (HV), the lower value (LV) and the mean value (MV) have to be all values that are associated to the word per (for example: percents, averages, costs)
2. You select a quantity that overlaps between the higher, lower and mean values.



Now here the question gives us two solutions of milk and water,

Solution 1 - W : M -----> 1 : 2 -----> W = 1/3 and M = 2/3

Solution 2 - W : M -----> 2 : 5 -----> W = 2/7 and M = 5/7

Now we need to mix these two in the ratio of 1 : 4, so we have been given HV - MV : MV - LV = 1 : 4

Drawing the mixture diagram for solution 1



Drawing the mixture diagram for solution 2



Combining these two ratios we get