Aptitude  Alligation or Mixture
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 Alligation or Mixture  Formulas
 Alligation or Mixture  General Questions
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture =  3   3x  + x  litres  
8 
Quantity of syrup in new mixture =  5   5x  litres  
8 
3   3x  + x  =  5   5x  
8  8 
5x + 24 = 40  5x
10x = 16
x =  8  . 
5 
So, part of the mixture replaced =  8  x  1  =  1  .  
5  8  5 
Since first and second varieties are mixed in equal proportions.
So, their average price = Rs.  126 + 135  = Rs. 130.50  
2 
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
Cost of 1 kg of 1^{st} kind Cost of 1 kg tea of 2^{nd} kind  
Rs. 130.50  Mean Price Rs. 153  Rs. x 
(x  153)  22.50 
x  153  = 1  
22.50 
x  153 = 22.50
x = 175.50
Suppose the can initially contains 7x and 5x of mixtures A and B respectively.
Quantity of A in mixture left =  7x   7  x 9  litres =  7x   21  litres.  
12  4 
Quantity of B in mixture left =  5x   5  x 9  litres =  5x   15  litres.  
12  4 

=  7  

9 
28x  21  =  7  
20x + 21  9 
252x  189 = 140x + 147
112x = 336
x = 3.
So, the can contained 21 litres of A.
Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1^{st} can =  3  litre, C.P. of 1 litre mix. in 1^{st} can Re.  3 
4  4 
Milk in 1 litre mix. in 2^{nd} can =  1  litre, C.P. of 1 litre mix. in 2^{nd} can Re.  1 
2  2 
Milk in 1 litre of final mix. =  5  litre, Mean price = Re.  5 
8  8 
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1^{st} can C.P. of 1 litre mixture in 2^{nd} can  

Mean Price





Ratio of two mixtures =  1  :  1  = 1 : 1. 
8  8 
So, quantity of mixture taken from each can =  1  x 12  = 6 litres.  
2 
By the rule of alligation:
Cost of 1 kg pulses of 1^{st} kind Cost of 1 kg pulses of 2^{nd} kind  
Rs. 15  Mean Price Rs. 16.50  Rs. 20 
3.50  1.50 
Required rate = 3.50 : 1.50 = 7 : 3.