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 :7:57:95:93:7

The problem involves the concept of mixtures and alligation, which is a rule that allows us to find the ratio in which two or more ingredients at a given price must be mixed to produce a mixture of a desired price.

Here's the step-by-step solution:

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

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

3. In vessel C, we want the mixture to be half milk and half water. So, the fraction of milk we want in vessel C is 1/2.

4. Now, we use the rule of alligation. We subtract the fraction of milk in vessel B from the fraction of milk we want in vessel C, and we get 1/2 - 2/5 = 1/10.

5. Similarly, we subtract the fraction of milk we want in vessel C from the fraction of milk in vessel A, and we get 4/7 - 1/2 = 1/14.

6. The ratio in which the liquids in both the vessels are mixed to obtain a new mixture in vessel C containing half milk and half water is therefore 1/10 : 1/14, which simplifies to 7:5.

So, the correct option is 7:5.