80 litres of a mixture of spirit and water in the ratio $7:9$ is present in a container A. 20 litres of the mixture is transferred to another container B. Then the container A is filled with 20 litres of water. Then 32 litres of the mixture is again transferred to container B. What is the ratio of water to spirit in the mixture in container B?

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**Solution:**

1. Initial quantity of spirit in mixture A:
   $$80 	imes \frac{7}{16} = 35 	ext{ L}$$

2. Initial quantity of water in mixture A:
   $$80 	imes \frac{9}{16} = 45 	ext{ L}$$

3. When 20 L of mixture is transferred from A to B, spirit and water transferred are:
   - Spirit: $$20 	imes \frac{7}{16} = 8.75 	ext{ L}$$
   - Water: $$20 	imes \frac{9}{16} = 11.25 	ext{ L}$$

4. After transferring 20 L from A, container A is filled with 20 L water. So new quantities in A:
   - Spirit: $$35 - 8.75 = 26.25 	ext{ L}$$
   - Water: $$45 - 11.25 + 20 = 53.75 	ext{ L}$$

5. New ratio of spirit to water in A:
   $$26.25 : 53.75 = 21 : 43$$ (dividing both by 1.25)

6. Now 32 L of mixture from A is transferred to B. Spirit and water transferred:
   - Spirit: $$32 	imes \frac{21}{64} = 10.5 	ext{ L}$$
   - Water: $$32 	imes \frac{43}{64} = 21.5 	ext{ L}$$

7. Total quantities in B after both transfers:
   - Spirit: $$8.75 + 10.5 = 19.25 	ext{ L}$$
   - Water: $$11.25 + 21.5 = 32.75 	ext{ L}$$

8. Ratio of water to spirit in B:
   $$32.75 : 19.25 = 131 : 77$$ (multiplying both by 4)

**Answer:** $131 : 77$

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