Question

Mixture and allegation theory for banking liquid replacement formula

Answer 1

I came across two methods which I found very handy in solving some types of mixture problems. So I thought of sharing it with the gc community.
here they are

Rule of Alligation
It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Mean Price: The cost price of a unit quantity of the mixture is called mean price.


Rule of Alligation

If two quantities are mixed, then



QuantityofcheaperQuantityofdearer=(C.P.)ofdearer−(MeanPrice)(MeanPrice)−(C.P.)QuantityofcheaperQuantityofdearer=(C.P.)ofdearer−(MeanPrice)(MeanPrice)−(C.P.)


Taking a simple example

In what ratio must rice at 9.30 /kg be mixed with rice at 10.80/kg so that the mixture be worth 10/kg?

C.P of cheaper=9.30
C.P of dearer=10.80
C.P of mean or mean price = 10.0

so putting the values in the formula
QcQd=Cd−CmCm−CcQcQd=Cd−CmCm−Cc

=10.80−1010−9.310.80−1010−9.3

=8:7 Ans