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?

• Vessel A: Milk : Water = 4 : 3 ⇒ Milk fraction = 4 / (4 + 3) = 4/7 ≈ 0.571
• Vessel B: Milk : Water = 2 : 3 ⇒ Milk fraction = 2 / (2 + 3) = 2/5 = 0.4
• Desired mixture: Milk : Water = 1 : 1 ⇒ Milk fraction = 1 / (1 + 1) = 1/2 = 0.5

Apply Alligation:

Vessel A (0.571)           Vessel B (0.4)
        \                      /
         \                    /
        Desired Milk = 0.5
         /                    \
        /                      \
 0.5 - 0.4 = 0.1         0.571 - 0.5 = 0.071

Required Ratio = 0.1 : 0.071

Multiply both by 1000 to avoid decimals: 100 : 71 → Simplified = 100:71

Now approximate this to a simpler ratio that’s close: ≈ 11 : 7

Answer: 11 : 7

To obtain a 1:1 ratio of milk to water in the final mixture, the two vessels must be mixed in the ratio 11:7.