The milk & water in two vessels A & B are in the ratio 4:3 & 2:3 resp. In what ratio, the liquids in both the vessels are mixed to obtain a new mixture in vessel C containing half milk & half water?

To solve this problem, we need to understand that the ratio of milk to water in the final mixture is 1:1.

Step 1: Determine the milk to water ratio in each vessel.

Vessel A: The ratio is 4:3, which means for every 4 parts of milk, there are 3 parts of water. So, the fraction of milk in vessel A is 4/(4+3) = 4/7.

Vessel B: The ratio is 2:3, which means for every 2 parts of milk, there are 3 parts of water. So, the fraction of milk in vessel B is 2/(2+3) = 2/5.

Step 2: Determine the milk to water ratio in the final mixture.

Vessel C: The ratio is 1:1, which means for every 1 part of milk, there is 1 part of water. So, the fraction of milk in vessel C is 1/(1+1) = 1/2.

Step 3: Use the rule of alligation to find the ratio in which the liquids from vessels A and B must be mixed.

The rule of alligation states that:

(Quantity from Vessel B) / (Quantity from Vessel A) = (Fraction of milk in A - Fraction of milk in C) / (Fraction of milk in C - Fraction of milk in B)

Substituting the values we found earlier:

(Quantity from Vessel B) / (Quantity from Vessel A) = (4/7 - 1/2) / (1/2 - 2/5)

Solving this equation gives us the ratio in which the liquids from vessels A and B must be mixed to obtain the desired mixture in vessel C.

After simplifying the equation, we get the ratio as 1:2.

So, the liquids from vessels A and B must be mixed in the ratio 1:2 to obtain a new mixture in vessel C containing half milk and half water.

To solve this problem, we need to understand that the ratio of milk to water in the final mixture is 1:1.

Step 1: Determine the milk to water ratio in each vessel.

Vessel A: The ratio is 4:3, which means for every 4 parts of milk, there are 3 parts of water. So, the fraction of milk in vessel A is 4/(4+3) = 4/7.

Vessel B: The ratio is 2:3, which means for every 2 parts of milk, there are 3 parts of water. So, the fraction of milk in vessel B is 2/(2+3) = 2/5.

Step 2: Determine the milk to water ratio in the final mixture.

Vessel C: The ratio is 1:1, which means for every 1 part of milk, there is 1 part of water. So, the fraction of milk in vessel C is 1/(1+1) = 1/2.

Step 3: Use the rule of alligation to find the ratio in which the liquids from vessels A and B must be mixed.

The rule of alligation states that:

(Quantity from Vessel B) / (Quantity from Vessel A) = (Fraction of milk in A - Fraction of milk in C) / (Fraction of milk in C - Fraction of milk in B)

Substituting the values we found earlier:

(Quantity from Vessel B) / (Quantity from Vessel A) = (4/7 - 1/2) / (1/2 - 2/5)

Solving this equation gives us the ratio in which the liquids from vessels A and B must be mixed to obtain the desired mixture in vessel C.

After simplifying the equation, we get the ratio as 1:2.

So, the liquids from vessels A and B must be mixed in the ratio 1:2 to obtain a new mixture in vessel C containing half milk and half water.