Ratios, Mixtures and Allegations

Ratio and mixture questions are common in every exams like bank jobs  exam conducted by ibps, state bank of india, competitive exams, ssc, staff selection commission exams, CAT- common aptitude test etc. 

Its not tough to learn this section. There is only need of practice class. 

Alligation or mixture 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.  It consist of two parts:-

Mean price

Cost price

Mean price is  a price of a unit quantity of the mixture.

What is formula for mixture/ alligation

(Quantity of cheaper) = (C.P. of dearer) - (Mean price)

(Quantity of dearer)       (Mean price) - (C.P. of cheaper)

C.P.  means cost price

                            

C.P. of a unit quantity                                       C.P. of a unit quantity 
of cheaper                                                          of dearer

So 

cheaper quantity : dearer =   (d-m ) : (m-c)

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Example:-

In what ratio must water be mixed with milk to gain 20 %  by selling the mixture at cost price?

Solution:-

Suppose cost price of 1 litre milk is = Rs 1

Than selling price of 1 l mixture     = Rs 1 as we are selling it on cost price

We got profit of  20 %

C.P. of 1 litre of mixture = Rs.[(100/120)* 1]=Rs.5/6

As C.P.  =  [(100/100+p)* S.P.]

                       C.P. of 1 litre of water                    C.P. of1litre ofmilk

                         0                                             Rs 1

                   (1- (5/6))= 1/6                                                    ((5/6)-0)=5/6

So therefore ratio of water and milk=

1/6 : 5/6