Quantitative Aptitude Notes Part 15( Mixture and allegation)

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Mixture and allegation

 

Alligation: This 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 the mean price.

Rule of Alligation:
If Two ingredients are mixed in a ratio , then
 =     
We present it under as
C.P.M.1 = Cost Price of First Materiel in a Mixture.
C.P.M.2 = Cost Price of Second Materiel in a Mixture.
C.P.M.3 = Cost Price of Mixture.
So,
C.P.M.1 : C.P.M.2 = ( C.P.M.1 – C.P.M.3 ) : ( C.P.M.2 – C.P.M.3 ).
OR,
(Cheaper quantity ) : ( Dearer quantity ) = ( d – m ) : ( m – c ).
m = mean price.
d = C.P of dearer.
c = C.P of cheaper.

Here is another important formula which is,
Consider a container contain x units, and from which we are taken out y units and replace it by water.
After that n operation,
the quantity of pure liquid = [ x ( 1 – y / x )n] units.
Here is some sub link of Examples about this topic which help you better understanding.

Example:
In what proportion must rice at 3.25 per kg be mixed with rice at Rs 3.80 per kg , So that the mixture be worth Rs 3.50 a kg ?
Answer:
=
=
Quantity of cheaper rice / Quantity of dearer rice = 30 / 25 = 6 / 5
So, They must be mixed in the ratio 6: 5 .

Example:
In a What ratio Wheat at Rs. 12.30 per kg be mixed with wheat 18.30 per kg so that the mixture be worth Rs.15 per kg?
Answer:
We know that: (Cheaper quantity): (Dearer quantity)=(d – m): (m – c).

C.P.M.1=(Cost price of First material) = 12.30 = 1230
C.P.M.2=(Cost price of Second material) = 18.30 = 1830
M.P = (Mean price of both Material) = 1500
So,
(C.P.M.1 – M.P):(C.P.M.2 – M.P)= (1500 – 1230):(1500 – 1830) = 270 : 330 = 9 : 11.

Required Ratio of both materials is 9: 11.

 

Example:
A goldsmith has two qualities of gold one of 14 carats and another of 17 carats purity . In what proportion should he mix both to make an ornament of 16 carats purity?
Answer:
We know that:  =

=  =
= =
So , They must be mixed in the ratio 1 : 2 .

Example:
400 gm of rice solution has 30% rice in it  . How much rice should be added to make it 50% in solution?
Answer:
The already existing solution has 30% rice .
So the other solution has 100% rice ,
We know that:  =
= = .
The two mixtures added in ratio 5 : 2 .
required rice is = 400 x = 160 gm .
Shortcut tricks:
solution
400 = 160 gm .

Example:
In What ratio stone be mixed with rice so as to gain 40% by selling at C.P?
Answer: Let be
C.P of pure rice is = 1
and S.P of mixture is = 1
than % profit = 40%

C.P in a mix is = 1 / 140 X 100 = 5 / 7.
here we applied alligation formula
C.P.1 = 1(rice).
C.P.2 = 0(stone).
M.P(mix) = 5 / 7.
= ( C.P.1 – M.P ):( C.P.2 – M.P ) = 2 / 7 : 5 / 7 = 2 : 5.

So Ratio between Rice and Stone to gain 40% Profit = 2 : 5.

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