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
 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
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 :
= 
( 
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 :
 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 ?

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 ?

In what ratio must water be mixed with oil costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre ?
Answers :
1 = 5 : 4, 2 = 3 : 1, 3 = 1 : 2
