# 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 kg

Please 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 12.916

We 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

1. 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
2. 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 = 3.832

So 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) = 12.916

Took 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.

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