Step 1: Understanding the problem.
The capacity of the evaporator is given as 4000 kg of solid caustic soda per day. The solids are being concentrated from 10% to 35% solids, which means the amount of water removed is the difference between the initial and final weights of water.
Step 2: Calculation.
The weight of the solids in the initial and final states can be calculated. The amount of water evaporated is the difference between the initial and final water contents.
\[
\text{Water evaporated} = \text{Initial water} - \text{Final water} = 4000 \times \left( \frac{10}{90} \right) - 4000 \times \left( \frac{35}{65} \right)
\]
\[
\text{Water evaporated} \approx 28571 \, \text{kg per day}.
\]
Final Answer: \[ \boxed{\text{A) 28571}} \]
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