The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?

Milk in 1-litre mixture of A = 4/7 litre. 

Milk in 1-litre mixture of B = 2/5 litre. 

Milk in 1-litre mixture of C = 1/2 litre.

By rule of alligation we have required ratio X:Y   

   X                  :                 Y  

  4/7                                2/5  

           \                      /

              (Mean ratio)
                   (1/2) 

           /                      \

 (1/2 – 2/5)     :       (4/7 – 1/2)  

    1/10                      1/1 4 

So Required ratio = X : Y = 1/10 : 1/14 = 7:5