Friday, 25 November 2016

Mixture and Alligations

Mixture and Allegations (Quantitative Aptitude) for Bank PO, Clerk, SSC CHSL, CGL and other competitive exams  simple mixture , compound mixture , allegations  and rule of allegations ,removal and replacement.


Allegations is the rule of find the proportion in which the two or more quantities at the produce a mixture at a given price.

Simple mixture 

When two different ingredients are mixed together , it is know as a simple mixture.

Compound Mixture

When two or more simple mixtures are mixed together to form another mixture , it is know as a compound mixture.

Rule of Allegation 

If two quantities are mixed in a ratio , then.

Quantity of cheaper / Quantity of dearer = CP of dearer - Mean price / Mean price - CP of cheaper

Application of Allegation Rule

1. To find the mean value of a mixture when the prices of two or more ingredients , which are mixed together and the proportion in which they are mixed are given.

2. To find the proportion in which the ingredients at given price must be mixed at a given price.

Allegation Rule for compound mixture

Remember that in compound mixture, same mixture of ingredients are mixed together in different proportion to make a new mixture.

Let mixture 1 has ingredients A and B in ratio a:b.
and mixture 2 has ingredients A and B in ratio x:y.
Now, M unit of mixture 1 and N unit of mixture 2 are mixed to form compound mixture. Then , in the resultant mixture , the ratio of A and B is

1. Quantity of ingredient A = qA / q= M (a / a+b)+N(x / x+y) / M (b / a+b)+N(y/x+y).
     Quantity of A in resultant mixture = qAqA + qB × (m + n ).

2. When qA and  qB are know and m and n have to be found out

•Quantity of Mixture 1 / Quantity of Mixture 2 = Q1 / Q2  = (x / x+y) - (qA / qA + qB)  /  (qA / qA + qB) - (a / a+b).

And ,
Quantity of mixture 1 = Q1 /  Q1 + Q2  =  Quantity of resultant mixture.
Quantity of mixture 2 = Q2  Q1 + Q2 = Quantity of resultant mixture.

Removal and Replacement

1. Let a vessel contains Q unit of mixture of ingredients A and B , from this , R unit of mixture is taken out and replaced by an equal amount of ingredient B only.

If this process is repeated n times , then after n operations

Quantity of A left / Quantity of A originally present = Q(1-R/Q)n

and Quantity of B left = Q - Quantity of A left

2. Let a vessel of B left = Q-Quantity of A only.From this R unit of ingredient A is taken out replaced by an equal amount of ingredients B.

If this process is repeated n times , then after n operations , 

Quantity of A left = Q (1-R/ Q)n

Quantity of B = 1 - Quantity of A left.

• If in x litres mixture of A and B , the ratio A and B is a:b, the quantity of B to be added in order to make the ratio c:d is x(ad - bc/ c (a+b).

• If x glasses of equal size are filled with a mixture of milk and water.The ratio of milk and water in each glass are as follows: a1: b1,a2 :b2, a3: b3 ,--------ax:bx.

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