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]
= 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.
Alligation and Mixtures: Next Tests: