Final answer:
To find the correct ratio to mix two milk and water mixtures to achieve an even milk to water ratio, we use the method of allegation. The mixtures in vessels A and B must be combined in the ratio of 7:10 to achieve a final mixture containing half milk and half water. The correct answer is option a.
Step-by-step explanation:
To solve for the ratio in which two mixtures of milk and water must be combined to form a new mixture containing half milk and half water, we can use the method of allegation. Vessel A has a mixture in the ratio of 4:3 (milk to water), and vessel B has a mixture in the ratio of 2:3.
Let's set the desired ratio of milk to water as 1:1, since we want a mixture with half milk and half water.
We subtract the milk content of each vessel from the desired milk content of 1/2 (the '1' in the 1:1 ratio, representing 50% milk).
This gives us:
- For A: 4/(4+3) - 1/2 = 1/7
- For B: 2/(2+3) - 1/2 = -1/10
Ignoring the signs, we now have the direct inverse ratio of the quantities of mixtures from vessels A and B that we need: 1/7 to 1/10, which is 10:7 when scaled to whole numbers.
However, keep in mind that we actually need to add these mixtures in the opposite ratio because the differences we calculated indicate how much less or how much more milk is in each mixture compared to the desired 50%.
Therefore, the correct ratio to mix the two given mixtures to achieve a milk to water ratio of 1:1 is in the ratio of 7:10, which simplifies to option (a) 7:5.