Average Mixture and Alligation Question

A shopkeeper mixes 3 varieties of rice costing rs 10, rs 12 and rs 17 per kg.
Which of the following can represent a possible ratio in which the 3 varieties are mixed , if the trader makes a profit of 20% by selling the mixture @ 15.50 per kgPlease solve it using ALLIGATION only

@deepalis727
We have cost price of various Rice types as 10, 12 and 17
We need to mix them so that trader makes a profit of 20% if sold at 15.50 rs.
As the all rice types are represented in terms of CP, we need to express the final price also as CP
15.50 = 1.20 x CP
CP = 15.50/1.20 = 12.916
So, we need to mix 10, 12 and 17 to get 12.916We are aware of the problems which use 2 mixtures and this has 3. So we will use the same allegation but in a slight different way. This would make your life easier while dealing with allegation problems involving 3 quantities
First write the terms in ascending or descending order
Now we know, 12.916 is between 12 and 17. So we will write it as below
Now just apply the usual allegation trick for 2 quantities
Now comes the difference. We need to do two things
 For the place which is marked as Question mark. Just put the same value which we got at the right side. Which is 17  12.0916 = 4.084
 We need to make 10 part of this equation and to do that connect 10 to the required mean value (here 12.916) and then where will we write it ? Just write it like the usual allegation, (12.916  10 = 2.916) along with the value already present there. In this case, 12.916  12 = 0.916
Now what should we do with the two values present at the same spot.. ? Just add it.
So we get 0.916 + 2.916 = 3.832So our required ratio is 4.084 : 4.084 : 3.832
Just to cross check:
So if we mix 10, 12 and 17 in the above ratio, mean should be
(4.084 x 10 + 4.084 x 12 + 3.832 x 17)/(4.084 + 4.084 + 3.832) = 12.916Took some time here because of detailed explanations and not so friendly calculations. During exams, you will solve this one in less than a minute :)
Also, it would be best just to check with options in similar questions.

Thanks a lot @zabeer