Short Answer 
The initial water transferred from container A to B is 11.25 L, followed by a refill that maintains the total volume at 80 L. After a second transfer of 32 L, the final ratio of water to spirit in container B is simplified to 77:131.
Step 1: Determine the Initial Amount of Water Transferred
Firstly, you need to calculate the amount of water in the initial transfer from container A to container B. The mixture in container A has a spirit to water ratio of 7:9 in an 80 L mixture. To find the fraction of water, use the formula:
- Water fraction = 9 / (7 + 9) = 9 / 16
- When transferring 20 L of this mixture, the amount of water is: (20 L) * (9/16) = 11.25 L.
Step 2: Update the Mixture in Container A
Next, after transferring the initial 20 L mixture, container A is refilled with 20 L of water. This changes the total volume of liquid and the proportion of water within the mixture. You can calculate the updated fraction of water using:
- New total volume in A = 80 L (initial) – 20 L (transferred) + 20 L (refill) = 80 L.
- The new fraction of water after the refill would be derived from the previous water volume plus the refill.
Step 3: Calculate the Final Ratio of Water to Spirit in Container B
Finally, transfer 32 L of the mixed solution from container A to B and calculate the total water now in container B. The water amount from this transfer can be computed as follows:
- Water from second transfer = (32 L) * (43/64) = 21.5 L.
- Total water in B now is: 11.25 L (initial) + 21.5 L = 32.75 L.
- The total spirit in container B after transfers is: (20 L + 32 L) – 32.75 L = 19.25 L.
- The final ratio of water to spirit in container B is 32.75 L : 19.25 L, which simplifies to 77:131.