The ratio of milk to water in mixture A is $9:5$. The quantity of milk in mixture B is 20\% more than that in mixture A, and the quantity of water in mixture A is 25\% more than that in mixture B. If the total quantity of water in both mixtures combined is 54 liters, what is the total quantity of mixture A?

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**Solution:**

1. Let the quantity of milk in mixture A be $9l$ liters and water be $5l$ liters, since the ratio of milk to water is $9:5$.

2. Quantity of milk in mixture B is 20\% more than in mixture A:
   $$	ext{Milk in B} = 9l 	imes \frac{120}{100} = 10.8l$$

3. Quantity of water in mixture A is 25\% more than in mixture B, so:
   $$	ext{Water in A} = 5l = 1.25 	imes 	ext{Water in B} \implies 	ext{Water in B} = \frac{5l}{1.25} = 4l$$

4. Total water in both mixtures is given as 54 liters:
   $$5l + 4l = 9l = 54 \implies l = 6$$

5. Total quantity of mixture A is:
   $$9l + 5l = 14l = 14 	imes 6 = 84 	ext{ liters}$$

**Answer:** 84 liters

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