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To solve this problem, let’s use the concept of weighted averages to mix water at different temperatures. We need to find the right proportions of water at \(40^\circ\) and \(25^\circ\) to get \(90\) liters of water at \(30^\circ\).

### Step-by-Step Solution

1. **Set up the equations:**
   Let:
   - \( x \) be the amount of water (in liters) at \(40^\circ\).
   - \( y \) be the amount of water (in liters) at \(25^\circ\).

   We need:
   \[
   x + y = 90
   \]
   to get a total of \(90\) liters of water.

2. **Set up the temperature balance equation:**
   The desired final temperature \(T_f\) is \(30^\circ\). We use the concept of a weighted average temperature, which gives us the equation:
   \[
   40x + 25y = 30(x + y)
   \]

3. **Substitute the total amount condition:**
   Substitute \(x + y = 90\) into the temperature balance equation:
   \[
   40x + 25y = 30 \times 90
   \]
   Simplify the right side:
   \[
   40x + 25y = 2700
   \]

4. **Solve the system of equations:**
   Now we have two equations:
   \[
   x + y = 90
   \]
   \[
   40x + 25y = 2700
   \]

   Solve the first equation for \(y\):
   \[
   y = 90 - x
   \]

   Substitute \(y = 90 - x\) into the second equation:
   \[
   40x + 25(90 - x) = 2700
   \]
   Expand and simplify:
   \[
   40x + 2250 - 25x = 2700
   \]
   \[
   15x = 450
   \]
   \[
   x = 30
   \]

   Substitute \(x = 30\) back into the equation \(y = 90 - x\):
   \[
   y = 90 - 30 = 60
   \]

5. **Conclusion:**
   To obtain \(90\) liters of water at \(30^\circ\), we need:
   - \(30\) liters of water at \(40^\circ\)
   - \(60\) liters of water at \(25^\circ\)

### Answer:
The correct answer is **(d) 30 liters of water at the temperature of 40°**.

Would you like further clarification on any part?

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### Related Questions
1. What is the formula for mixing different temperatures to achieve a desired average temperature?
2. How can you apply weighted averages to solve real-life problems?
3. What happens if we change the desired final temperature in the problem?
4. How would you solve this if the total volume was different?
5. What would be the effect of using an unequal amount of hot and cold water?

### Tip
When mixing substances with different temperatures, setting up a temperature balance equation with weighted averages is essential for finding the correct proportions.

We have water at the temperature of 40° and water at the temperature of 25°. To obtain 90l of water at the temperature of 30°, we need:

a. 45l water at the temperature of 40°
b. 60l water at the temperature of 40°
c. 40l water at the temperature of 40°
d. 30l water at the temperature of 40°

Learn how to solve a problem involving the mixing of water at different temperatures. This step-by-step solution covers the use of weighted averages and setting up a system of equations to find the correct proportions. Ideal for students in Grades 8-10.

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