Alligation and Mixture 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.10⅔ 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 10x = 3 × 36 or x = 10.8 kg.

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Alligation and Mixtures:
Formula:                Alligation and Mixtures Formulas
Solved Examples:  Solved Examples: Set 01     Solved Examples: Set 02
Practice Test:         Practice Test: 01