# Alligation and Mixture-Short Tricks 1

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 ?