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

Direct Formula / Rule 1 :

• Theorem: The proportion in which sugar at Rs. x per kg must be mixed with rice at Rs. y per kg, so that the mixture be worth Rs. z a kg, is given by

 = ( y - z ) z - x

• Example :

• The proportion in which sugar at Rs. 3.10 per kg must be mixed with sugar at Rs. 3.60 per kg, so that the mixture be worth Rs. 3.25 a kg ?

• Detail Method : Let the required ratio be x. y.
As per Question,
310x + 360y = 325(x+y)
or 310x + 360y = 325x + 325y
325x - 310x = 360y - 325y
150x = 350y
15x = 35y
3x = 7y
 = x : 7 y 3
so x : y = 7 : 3    [here y goes to left side & 3 goes to right side]

• Ailigation Method : By the rule of alligation we have :  C.P.of 1 kg cheaper sugar C.P.of 1 kg dearer sugar
 (310 paise) Mean price(325 paise) (360 paise) 35 15
So, ratio of 1st and 2nd quantities = 35 : 15 = 7 : 3
so, they must be mixed in the ratio of = 7 : 3

• Quicker Method : Here you can use direct formula :
 = ( y - z ) z - x
 = ( CP of dearer - Mean Price ) Mean Price - CP of cheaper
 = ( 3.60 - 3.25 ) = ( 0.35 ) 3.25 - 3.10 0.15
so, they must be mixed in the ratio of = 7 : 3

Exercise :
1. In what proportion must rice at Rs 21 per kg be mixed with rice at Rs 28 per kg, so.that the mixture be worth Rs. 25 a kg ?
2. In what ratio, must coffee at Rs. 62 per kg Is mixed With coffee at Rs. 72 per kg so that the mixture must be worth RS. 64.50 per kg ?
3. In what ratio must water be mixed with oil costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre ?