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? Options : 7:5 7:9 5:9 3:7

The problem involves the concept of mixtures and alligation, which is a faster method to solve these types of problems.

Here are the steps to solve the problem:

1. In vessel A, the ratio of milk to water is 4:3. So, the percentage of milk in vessel A is 4/(4+3) = 4/7 = 57.14%.

2. In vessel B, the ratio of milk to water is 2:3. So, the percentage of milk in vessel B is 2/(2+3) = 2/5 = 40%.

3. In vessel C, we want the mixture to be half milk and half water, so the percentage of milk should be 50%.

4. Now, we use the method of alligation. We subtract the smaller percentage from the desired percentage and the desired percentage from the larger percentage.

   57.14% - 50% = 7.14% 50% - 40% = 10%

5. So, the ratio in which the liquids from vessels A and B should be mixed is 7.14:10, which simplifies to approximately 7:10.

However, this option is not available in the given options. There might be a mistake in the problem or the options provided.