MIXTURE AND ALLIGATION FORMULA
What is a Mixture?
A mixture contains two or more ingredients of certain of certain quantity mixed together to get the desired quantity. This quantity is expressed as ratios or percentage.
Mixture is when two varieties of rice are mixed to form a new variety of rice.
What is an Alligation?
Two ingredients A and B of price x and y respectively are mixed and the price of the resultant mixture is M (mean price), the ratio (R) in which ingredients are mixed is called, the rule of the alligation
An alligation is the rule that enables us to find the ratio where two or more ingredients at a given price or value should mix to produce a mixture at a given price (Value or Strength).
Formulas for Mixtures and alligation questions
Pictorial representation of Mixtures and Alligation
Example 1: Mixtures and Alligation Questions
Question: How much salt at 42 paise/kg will mix with 25kg salt at 24 paise/kg, to earn a profit of 25% by selling the mixture at 40 paise /kg?
Th question is based on a combination of two different varieties of salt to obtain a mixture at the given price.
In this question, we have to find the quantity of salt costing 42 paise i.e., mixed.
So, we need to find the ratios of the quantity to find the quantity of salt i.e., mixed.
First, we need to find the price of the mixed salt, that is
Profit = 25%
Selling Price = 40 paise/kg
Cost of the Mixture = 32 paise
Use the pictorial representation method to find the ratios.
The ratio = 4 : 5
Quantity(dearer) : Quantity (Cheaper) = 4 : 5
Again, Quantity(dearer) : 25 = 4 : 5
Furthermore, Quantity(dearer) x 5 = 4 x 25
Then, Quantity(dearer) = 100/5
And at last, Quantity(dearer) = 20kg
Hence, To make a new salt mixture, 20kg of dearer quantity will be mixed with 25kg of cheaper quantity
Example 2: Mixtures and Alligation Questions
Question: A merchant has 840kg of rice, part of which he sells at 9% profit and the rest at 16% profit. He must gain 12% profit on the whole. Find the quantity sold at 16% profit?
By applying the alligation rule on the profit percentages
Quantity (sold at 9% profit): Quantity (sold at 16% profit) = 4 : 3
840: Quantity (sold at 16% profit) = 4 : 3
Quantity (sold at 16% profit) = (3 / 7) x 840 (by the basis of ratio and proportion, we need to take the whole part i.e. 4 + 3 = 7)
Quantity (sold at 16% profit) = 360Kg.
Hence, It incur 16% profit to sell 360 kg
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