**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.