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?

• A. 8:3
• B. 11:7
• C. 6:7
• D. 7:5

Answer: (D)

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