To solve this problem, let's follow a step-by-step approach to determine how much water can be pumped from the aquifer to balance the water budget.
1. Identify Given Values:
- The aquifer receives a precipitation input: [tex]\(40 \, \text{m}^3\)[/tex].
- The aquifer loses water through natural movement: [tex]\(10 \, \text{m}^3\)[/tex].
2. Formulate the Problem:
- We need to determine the amount of water that can be pumped out to balance the water budget in the aquifer. Balancing the budget means the amount of water pumped should equal the net gain of water after accounting for losses.
3. Calculate the Net Gain of Water:
- Subtract the water lost through natural movement from the precipitation received:
[tex]\[
\text{Net Gain} = \text{Precipitation} - \text{Natural Loss}
\][/tex]
[tex]\[
\text{Net Gain} = 40 \, \text{m}^3 - 10 \, \text{m}^3 = 30 \, \text{m}^3
\][/tex]
4. Determine the Amount of Water to Pump:
- The amount of water that can be pumped from the aquifer while balancing the budget is equal to the net gain of water:
[tex]\[
\text{Water to Pump} = 30 \, \text{m}^3
\][/tex]
5. Multiple Choice Answer:
- Among the given options, [tex]\(30 \, \text{m}^3\)[/tex] is the correct answer.
The final result is:
[tex]\[
\boxed{30 \, \text{m}^3}
\][/tex]
