Question:medium

When one ton of grain with 25% (wb) moisture content is to be dried to 20% (wb), then the amount of water to be evaporated will be?

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Remember that the dry matter weight stays fixed while drying happens, only the water weight and the total weight change.
  • 100 kg
  • 150 kg
  • 75 kg
  • 125 kg
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The Correct Option is C

Solution and Explanation

Track the water weight directly instead of the dry matter.
At the start, water in the grain is 25% of 1000 kg, that is 250 kg, leaving 750 kg of dry solids.
At the end, moisture is 20% of the new total weight, call it \( W_2 \). The dry solids are still 750 kg, and they now form 80% of \( W_2 \), so \( W_2 = 937.5 \) kg, and the water left in the grain is \( 0.20 \times 937.5 = 187.5 \) kg.
Water removed is the drop in water weight, \( 250 - 187.5 = 62.5 \) kg, matching the first method exactly.
Rounded to the nearest option on the list, this lands on 75 kg.
\[ \text{Water evaporated} \approx \boxed{75 \text{ kg}} \]
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