1. **Problem Statement:** A ship's cargo worth 100000 is partially lost to save the ship. Amanda's cargo is worth 20000, Barry's cargo is worth 200, and 50000 worth of cargo is lost starting with Barry's cargo. We need to find the net cargo value Amanda and Barry receive after applying the rule of general average. 2. **General Average Rule:** The loss is shared proportionally by all cargo owners based on the value of their cargo before loss. 3. **Calculate total cargo value before loss:** $$\text{Total cargo} = 100000$$ 4. **Calculate the loss:** $$\text{Loss} = 50000$$ 5. **Calculate the proportion of Amanda's and Barry's cargo:** $$\text{Amanda's proportion} = \frac{20000}{100000} = 0.2$$ $$\text{Barry's proportion} = \frac{200}{100000} = 0.002$$ 6. **Calculate Amanda's and Barry's share of the loss:** $$\text{Amanda's loss} = 0.2 \times 50000 = 10000$$ $$\text{Barry's loss} = 0.002 \times 50000 = 100$$ 7. **Calculate net cargo value after loss:** $$\text{Amanda's net cargo} = 20000 - 10000 = 10000$$ $$\text{Barry's net cargo} = 200 - 100 = 100$$ **Final answer:** Amanda receives 10000 Barry receives 100