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Alligation and Mixture

Mixture: Mixing of two or more than two type of quantities gives us a mixture.

Alligation : Alligation is a 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:
If the ratio of milk to water in a mixture is a:b. if x litre of water is added to a mixture, then the ratio of milk to water becomes a:c, then
Quantity of milk in a mixture is ax/(c-b) litre
Quantity water in mixture is bx/(c-b) litre

If the ratio of income of two persons is a:b and ratio of their expenses is c:d and ratio of their expenses is c:d and each person saves x Rs. then
income of first person = xa(d-c)/(ad-bc)

income of Second person = xb(d-c)/(ad-bc)

Eg1:
A mixture contains milk and water in the ratio of 4:3.If 5L of water is added to the mixture,the ratio becomes 4:5,the quantity of milk in the given mixture is?

Explanation-
Given, a:b=4:3 i.e.,a=4,b=3
and a:c=4:5
i.e.,a=4,c=5 and x=5
Then,quantity of milk=ax/(c-b)
=(4*5)/(5-3)
=10 L
Eg2:
The ratio of the incomes of Raman and Gagan is 4:3 and Ratio of their Expenditures is 3:2. If each person saves Rs 2500.Then,Raman’s Income is
Explanation- a=4,b=3,d=2
and x= 2500 Rs.
Therefore,Income of Raman = (x(d-c)/ad-bc)*a
= ((2500(2-3))/(8-9))*4
= 10000 Rs.