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**Alligation**** and
Mixtures Important formulas:**

**Alligation**

**and Mixtures Important formulas:**

**1. 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.

Or, Alligation is an old and practical method of
solving arithmetic problems related to mixtures of ingredients.

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

**3. Rule of Alligation:**If two ingredients are mixed, i.e. if

*‘c’*kg of cheaper thing mixed with ‘

*d*’ kg of dearer thing and we get ‘m’ kg of mixture, then

The Preparation for the solution is like this.

Therefore, (Cheaper quantity): (Dearer quantity) = (d - m): (m - c).

**4.**Suppose a container contains ‘

*x*’ units of liquid from which ‘

*y*’ units are taken out and replaced by water. After ‘n’ operations the quantity of pure liquid=[

*x*{1- (

*y/x*)}

^{n}] units.

__Solved Examples:__

__Example: 01__**How much water must be added to 60 litres of milk at 1½ liter for Rs. 20, so as to have a mixture worth Rs.10**

**⅔**

**a liter?**

__Solution:__
C.P. of 1 liter of milk = Rs. (20 × 2/3) = Rs. 40/3

Therefore, Ratio of water and milk = (8/3): (32/3) = 1:
4

Hence, Quantity of water to be added
to 60 litres of milk = [(1/4) × 60] Liters

= 15 Liters.

__Example: 02__**How many kgs of wheat costing Rs. 8 per kg must be mixed with 86 kg of rice costing Rs. 6.40 per kg so that 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg ?**

__Solution:__
S.P. of 1 kg mixture = Rs. 7.20, Gain = 20%.

Therefore, C.P. of 1 kg mixture = Rs. [(100/120) × 7.20]
= Rs. 6.

By the rule of alligation, we have:

Wheat of 1st kind: Wheat of 2nd kind = 60: 200 = 3:
10.

Let ‘x’ kg of wheat of 1st kind be mixed with 36 kg of
wheat of 2nd kind.

Then, 3: 10 =

*x*: 36 or 10*x*= 3 × 36 or*x*= 10.8 kg.**Alligation and Mixtures: Next Tests:**