HOW TO SOLVE MIXTURE AND ALLIGATION PART 2TIPS,TRICKS AND SHORTCUTS
HOW TO SOLVE MIXTURE AND ALLIGATION PART 2TIPS,TRICKS AND SHORTCUTS
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INTRODUCTION:
Hi Aspirants today we are going to discuss on a topic Mixture and Alligation. This topic carries 1 mark in prelims and 2 mark in mains exam.
MIXTURE:
When two or more components are mixed together then it is known as Mixture
Mixture is of two types they are:
1.Simple Mixture:When two or more different ingredients are mixed together,a simple mixture is formed
2.Compound Mixture:When two or more simple mixtures are mixed together, a compound mixture is formed.
ALLIGATION:
It enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price.
Where M=Mean Value which is between X and Y, X=Cheaper Price, Y=Price higher than the Mean Value
Before Looking into Mixture and Alligation look into Ratio and Proportions.
Read About Ratio and Proportions Part 1
TYPE 1:
BASED ON THREE INGREDIENTS OR THREE RATIO’S:
1.The Grocer sells apples of 3 varieties whose price per kg’s are Rs.40,Rs.60 and Rs. 90 .If he sells 1kg of apple by missing all these 3 varieties for Rs.80 what is the ratio by which these varieties are to be mixed?
1^{st} variety  3^{rd} variety 
2^{nd} variety

1  4  
2  1 
Ratio’s by which these 3 Qualities are missed are=1:2:4
2.Tea worth Rs.126 per kg and Rs.135 per kg are mixed with a third variety in the ratio 1:1:2.If the mixture is worth Rs.153 per kg, the price of the third variety per kg will be?
Given that the tea worth Rs.126 and Rs.135 per kg is mixed in the ratio 1:1.
Therefore price for 1kg= = Rs.130.50
Now we have two price 130.50 and the price of the third variety is X
The price of the third variety=Rs.175.50
3.There are three vessels of equal capacity holds milk and water in the ratio of 1:2,2:3 and 1:4if the content of all the three vessel s are mixed in asingle vessel then.Find the ratio of milk and water in the new vessel?
Here there are three ratio’s
1:2=3Part
2:3=5Part
1:4=5Part
Lcm =15Litres
Milk  Water 
5Litres  10Litre 
6Litre  9Litre 
3Litre  12Litre 
14Litres  31Litre 
The new Ratio is 14:31
TYPE 2:
BASED ON REMOVING AND ADDING SOME QUANTITY :
1)How much water must be added to 60 litres of milk at 1.5 litre for Rs.20,So as to have a mixture worth Rs.10 2/3 per litre?
C.P for 1.5 litre of milk =Rs.20
C.P for 1 litre of milk=Rs.40/3
C.P for 1 litre of water=Rs.0
Given Mean value=Rs.32/3
8/3 : 32/3= 1:4
Therefore water in the mixture in 60 litres is (1/5)*60=12 litres
2)In a 729 litres mixture of milk and water ,the ratio of milk to water is 7:2.To get a new mixture containing milk and water in the ratio 7:3,the amount of water to be added is?
729 

7x 
2x 
9x=729 x=81
Old Mixture New Mixture
7:2 7:3
Already the mixture contains water in the proportion 2x and the new mixture contains water in the proportion 3x .So x quantity of water is added to the mixture .Therefore 81 litres of water is added to the new mixture.
3)8 litres are drawn from a cask filled with wine and is then filled with water .This operation is performed three more times.The ratio of the quantity of wine now left in the cask to that of the total solution is 16:81.How much wine does the cask originally ?
When the final amount of solute that is not replaced calculated as:
Initial Amount * (Volume After Removal/Volume After Replacing)^n
Final ratio of solute not replaced to total is
Initial Ratio * (Volume After Removal/Volume After Replacing)^n
Here let us assume the initial value is 1 then Wine .Let the Quantity of wine in the cask originally be x
Therefore
1* [(x8)^4/x]
=[16/81]
x=24litres
Wine originally in the cask is 24 Litres
4)A vessel contains mixture of liquids A and B in the ratio 3:2.When 20 litres of the mixture is taken out and replaced by 20litres of liquid B,the ratio changes to 1:4.How many litres of liquid A was there initially present in the vessel?
Original ratio=3:2
3/5 * (5X20)/5x=1/4
X=6 then the liquid A in the vessel =3X=3*6=18Litres
IMPORTANCE OF MIXTURE AND ALLIGATION:
Mixture and Alligation is used in other Miscellaneous Topic such as
Ratio and Proportion
Time and Distance
You can reduce the time taken to solve the problem if you use Mixture and Alligation Method
YOU MAY ALSO LIKE TO READ:
TRICKS TIPS SHORTCUTS FOR ALL THE TYPES OF PROBLEMS BASED ON RACES
TIPS TRICKS AND SHORTCUT METHOD TO SOLVE BOATS AND STREAMS
3 comments
Okay my mistake
Hi Mam,
It is given as 10 2/3 in the question.
Type 2,question no:1 is incorrect.How the mean price became 32/3 from 10
Comments are closed.