Chapter - 15
MIXTURE AND ALLIGATION
What is a Mixture: The new product obtained by mixing two or more ingredients in a certain ratio is called a mixture of those particular ingredients.
Rule of mixture or Alligation:
1) The rule help us in finding the ratio in which two or more ingredients at certain prices must be mixed to produce a mixture at a given price.
2) The rule also helps to find out the mean or average value of mixture when he prices of two or more ingredients which may be mixed together and the ratio in which they are mixed are given.
When two ingredients at given prices are known, then the ratio in which these two are mixed to obtain a mixture of known price is given by
Hence Amount of Cheaper: Amount of dearer = (D – M) : (M – C)
Note : (1) This method can be used when percent, per hour, per km, per kg etc are being compared
(2) The CP of the unit quantity of mixture is called the mean price (M)
Example 1: In what ratio, wheat at Re 6.20 per kg be mixed with wheat at Rs 7.20 per kg, so that the mixture is worth Rs 6.50 per kg
Required ratio is 70 : 30 or 7 : 3
Example2: In what ratio Rice worth Rs 30 per kg should be mixed with rice w2orth Rs 32.5 per kg so that on selling the mixture at Rs 34.10 per kg, the profit is 10%.
Cost price of rice so that the profit is 10% when SP is 34.10
= 34.10 x Rs 31
The ratio in which rice is to be mixed is 1.5 : 1 Or 3 : 2
Example 3: The mixture of a certain quantity of milk with 16 litre of water is worth 0.75 per litre. If pure milk be worth 2.25 per litre, how much milk is there in the mixture.
Cost of water is Rs 0 per litre
Water : Milk = 1.50 : 0.75
or 2 : 1
or quantity of milk