Help needed with ratios

[numbernoob]

Question- Vessel A contains milk and Vessel B contains water. Initially, milk in Vessel A and water in Vessel B

is in ratio 2:3. 20% of the volume of Vessel A is poured in Vessel B and then half of the final​

volume of Vessel B is poured in Vessel A. The process is repeated again.​

Find the ratio of water in Vessel A to Vessel B.​

Options-

1. 3:7 ​

2. 7:3​

3. 7:43 ​

4. 43:7​

 

[JeffM]

Do you know algebra?

 

[Steven G]

Asking for help (as you did) and asking someone on the forum to do your problem for you are not the same.
Please read the posting guideline and submit a post following those guidelines. Thanks

 

[Dr.Peterson]

Question- Vessel A contains milk and Vessel B contains water. Initially, milk in Vessel A and water in Vessel B

is in ratio 2:3. 20% of the volume of Vessel A is poured in Vessel B and then half of the final​

volume of Vessel B is poured in Vessel A. The process is repeated again.​

Find the ratio of water in Vessel A to Vessel B.​

Options-

1. 3:7 ​

2. 7:3​

3. 7:43 ​

4. 43:7​

One way to do this (using only arithmetic) is just to assume some amount of each at the start, such as 200 L milk in A, 300 L water in B, and then keep track of how much of each is in each container through the process. Then find the ratio at the end.

But since they only ask for the ratio of the amounts of water (ignoring the fact that you couldn't separate the water from the milk!), you could ignore the milk entirely and just follow how much water there is in each place.

What method did you use? Show us your work, and we can help you finish it or fix it if necessary.

 

[HallsofIvy]

As Dr. Peterson suggested, assume there are 2 liters of milk in vessel A and 3 liters of water in vessel B. 20% of 2 is 2/5 or .4 liters so we pour 0.4 liters of milk into vessel B. There are now 3 liters of water and 0.4 liters of milk, a total of 3.4 liters of liquid, in vessel B. We now pour half of that back into vessel A so we pour 1.5 liters of water and 0.2 liters of milk back into vessel A. A had, before this, 1.6 liters of milk so after this it contains 1.8 liters of milk and 1.5 liters of water, a total of 3.3 liters of liquid while B now contains 1.5 liters of water and 0.2 liters of milk, a total of 1.7 liters. (As a check on our arithmetic notice that those still add up to 3.3+ 1.7= 5.0 liters of liquid- the first time I did this check I found I had made an error!)

Now do it again!