1. **Problem statement:** We need 8000 kg of paddy with moisture content 12% (dry basis, db). We have freshly harvested paddy with moisture content 20% (wet basis, wb) and want to find how many kg of this paddy to procure before drying. 2. **Understanding moisture content:** - Moisture content on dry basis (db) is defined as $M_{db} = \frac{W_{water}}{W_{dry}}$. - Moisture content on wet basis (wb) is defined as $M_{wb} = \frac{W_{water}}{W_{total}}$. 3. **Convert required moisture content from dry basis to wet basis:** Given $M_{db} = 0.12$, we use the relation: $$M_{wb} = \frac{M_{db}}{1 + M_{db}} = \frac{0.12}{1 + 0.12} = \frac{0.12}{1.12} \approx 0.1071$$ So, the required moisture content on wet basis is approximately 10.71%. 4. **Calculate dry matter in required paddy:** Total mass required = 8000 kg at 12% db moisture. Dry matter mass $W_{dry} = \frac{W_{total}}{1 + M_{db}} = \frac{8000}{1 + 0.12} = \frac{8000}{1.12} \approx 7142.86$ kg. 5. **Calculate mass of freshly harvested paddy to procure:** Fresh paddy moisture content $M_{wb} = 0.20$. Dry matter fraction in fresh paddy = $1 - M_{wb} = 0.80$. Let $W_{fresh}$ be the mass of fresh paddy to procure. Dry matter in fresh paddy = $0.80 \times W_{fresh}$. Since dry matter is conserved, $$0.80 \times W_{fresh} = 7142.86$$ 6. **Solve for $W_{fresh}$:** $$W_{fresh} = \frac{7142.86}{0.80} = 8928.57$$ **Final answer:** Approximately 8929 kg of freshly harvested paddy with 20% moisture (wb) must be procured to obtain 8000 kg of paddy at 12% moisture (db) after drying.