Alligation or Mixture -> Formula/Rule 3

Direct Formula / Rule 3 : Theorem: A mixture of a certain quantity of milk with 'L' litres of water is worth Rs x per litre. If pure milk be worth Rs y per litre, then the quantity of milk is given by : = L ( x ) litres. y - x Example : A mixture of a certain quantity of milk with 16 litres of water is worth 90 P per litre. If pure milk be worth 108 P per litre how much milk is there in the mixture? Detail Method : Let the quantity of milk be x litres.  (x + 16) 90 = x X 108 + 16 X 0 [because the price of water is 0 P]  Because Selling price of the mixture = 90 per kg given  or, 90x + 16 X 90 = 108x  or, 18x = 16 X 90  or, x = 80 litres.  ∴ The quantity of milk = 80 litres. Ailigation Method :  The mean value is 90 P and the price of water is 0 P. milk water 108 Mean price      90 0 90 - 0 108 - 90 = 90 : 18 By the Alligation Rule, milk and water are in the ratio of 5 : 1. ∴ quantity of milk in the mixture = 5 X 16= 80 litres. Quicker Method : Here you can use direct formula :  Quantity of milk in the mixture = 16 ( 90 )  = 16 X 5 = 80 litres. 108 - 90 Exercise : A mixture of a certain quantity of milk with 25 litres of water is worth Rs 2 per litre. If pure milk be worth Rs 12 per litre how much milk is there in the mixture? A mixture of a certain quantity of milk with 16 litres of water is worth Rs 3 per litre. If pure milk be worth Rs 7 per litre how much milk is there in the mixture? A mixture of a certain quantity of milk with 32 litres of water is worth Rs 1.50 per litre. If pure milk be worth Rs 4.50 per litre how much milk is there in the mixture?  Answers : 1 = 5 litres,   2 = 12 litres,   3 = 16 litres