Mixtures and Alligations

QUANT FOR CAT 09 : 

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Presents Mixtures & Alligations : 

Presents Mixtures & Alligations http://catathon.blogspot.com

What Kind Of Questions? : 

What Kind Of Questions? A mixture of certain quantity of Milk with 16L of water worth is 90 paise per litre. If pure milk costs 108 paise per litre, what is the amount of milk in the mixture?

Solution : 

Solution Pure Milk = 108 paise per litre Assume Water is free For 90 paise we get 90/108 = 5/6 litre of milk So the rest is water = 1/6 litre of water If 16 litres = 1/6 of whole quantity, Then 5/6 = 16 x 5 = 80 litres There are 80 litres milk in the solution

Straight Line Approach : 

Straight Line Approach N1 units of A at rate A1 per unit are mixed with N2 units of B at rate A2 per unit and the final mixture costs Aw per unit. N1 corresponds to A2 – Aw N2 corresponds to A1 – Aw

Solution By Straight Line Approach : 

Solution By Straight Line Approach A mixture of certain quantity of Milk with 16L of water worth is 90 paise per litre. If pure milk costs 108 paise per litre, what is the amount of milk in the mixture?

Problem : 

Problem A particular shade of green has 30% of yellow paint and 70 % blue paint by volume. How many gallons of yellow paint should be added to 70 gallons of this green paint to reduce the percentage of blue paint by 10 %? a) 7b) 23/3c) 10d) 32/3e) 35/3

Solution : 

Solution In 70 gallons green => Yellow forms 3/10 part => Blue forms 7/10 part After addition of x gallons of yellow, there will be 4/10 of yellow and 6/10 of blue as blue reduces by 10%.

Typical Problem : 

Typical Problem 4 liters of wine are drawn from a cask containing 40 liters of wine. It is replaced by water. This process is repeated 3 times. What is the final quantity of wine left in the cask? What is the ratio of wine to water finally?

Solution : 

Solution Wine 40 36=x 36-(36*4/40)=x-x/10 (x-x/10)-(x-x/10)/10 = x(1-1/10)2 x(1-1/10)3 Water 0 4=y y-y/10 y(1-1/10)2 y(1-1/10)3

General Formula : 

General Formula If a vessel contains “x” liters of milk and if “y” liters be withdrawn and replaced by water, then if “y” liters of the mixture be withdrawn and replaced by water, and the operation repeated ‘n’ times in all, then :

Practice Problem : 

Practice Problem A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture? (1)17 : 3  (2)9 : 1  (3)3 : 17  (4)5 : 3 Answer given in the exercise problems

Exercise : 

Exercise Visit http://www.catathon.blogspot.com For more problems on mixtures and alligations.

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