**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**

**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**

**Compound Mixture**

**Rule of Allegation**

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

**Application of Allegation Rule**

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

**Allegation Rule for compound 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 = q

2. When q

•Quantity of Mixture 1 / Quantity of Mixture 2 = Q

And ,

Quantity of mixture 1 = Q

Quantity of mixture 2 = Q

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

_{A /}**q**_{B }= M (*a*/*a*+*b*)+N(*x*/*x*+*y*) / M (*b*/*a*+*b*)+N(*y*/*x*+*y*)._{ }Quantity of A in resultant mixture = q_{A / }q_{A +}q_{B}× (*m*+*n*).2. When q

_{A}and q_{B}are know and m and n have to be found out•Quantity of Mixture 1 / Quantity of Mixture 2 = Q

_{1 }/ Q_{2 =}(*x***/***x*+*y*) - (q_{A / }q_{A +}q_{B) / }(q_{A / }q_{A +}q_{B)}- (*a***/***a*+*b*).And ,

Quantity of mixture 1 = Q

_{1 / }Q_{1 + }Q_{2 = }Quantity of resultant mixture.Quantity of mixture 2 = Q

_{2 / }Q_{1 + }Q_{2 = }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

Quantity of B = 1 - 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: a

_{1}: b_{1,}a_{2 :b}_{2, }a_{3}: b_{3 ,--------}a_{x}:b_{x}._{}**Go To Index of Section of Quantitative Aptitude**
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