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 Alligation or Mixture :-
 ::Important Formulas ::Examples

Direct Formula / Rule 18 :

• Theorem: If M kg of mixture, of which is a/b and the rest is B, be mixed with N kg of metal, of which is x/y and the rest is B, then the ratio of A to B in the mixture is given by
= [  M a + N x b y
]
 M ( 1 - a ) + N ( 1 - x ) b y

• Example :

• If 2 kg of metal, of which 1/3 is zinc and the rest of copper, be mixed with 3 kg of metal, of which 1/4 is zinc and the rest is copper, what is the ratio of zinc to copper in the mixture?

• Detail Method :
Quantity of zinc in the mixture
= 2(1/3)+3(1/4) = 2/3+3/4 = 8+9/12 = 17/12
Quantity of copper in the metal
= 3+2-17/12 = 5-17/12 = 43/12
So ratio = 17/12 : 43/12 = 17 : 43

• Quicker Method : Here you can use direct formula :
the required ratio
= [  2 X 1 + 3 1 3 4
]
 2 ( 1 - 1 ) + 3 ( 1 - 1 ) 3 4
 = 2/3 + 3/4 = 17 : 43. 4/3 + 9/4

Exercise :
1. If 1 kg of metal of which 1/3 is zinc and the rest copper be mixed with 2 kg of metal of which 1/4 is zinc and the rest copper, what is the ratio of zinc to copper in the mixture?
2. If 4 kg of metal of which 1/4 is zinc and the rest copper be 1 mixed with 5 kg of metal of which 1/5 is zinc and the rest copper, what is the ratio of zinc to copper in the mixture?
3. If 5 kg of metal of which 3/5 is zinc and the rest copper be mixed with 3 kg of metal of which 2/3 is zinc and the rest copper, what is the ratio of zinc to copper in the mixture?
4. Answers : 1 = 5 : 13,   2 = 2 : 7,   3 = 5 : 3

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