**Answer:**

To solve this question, we need to consider the relationship between energy and the fundamental units of length, mass, and time. Let's break down the solution into the following steps:

**Step 1: Understanding the Fundamental Units**
The fundamental units in the given system are length (L), mass (M), and time (T). Let's assume that the original energy is measured in units of (L^a)(M^b)(T^c), where a, b, and c are the exponents representing the relationship between energy and the fundamental units.

**Step 2: Given Information**
The given information states that the original energy is measured as 400 units. Therefore, we can write the equation as:
(400 units) = (L^a)(M^b)(T^c)

**Step 3: Doubling the Fundamental Units**
According to the question, the fundamental units of length, mass, and time are each doubled. This means that the new fundamental units will be 2L, 2M, and 2T, respectively.

**Step 4: Calculating the New Energy**
To calculate the new energy in the modified system, we need to determine the exponents (a', b', c') for the new fundamental units. Since each fundamental unit is doubled, we can express the new energy as:
(New Energy) = (L^(2a'))(M^(2b'))(T^(2c'))

**Step 5: Finding the Relationship Between the Old and New Energies**
To find the relationship between the old and new energies, we can equate the original energy (400 units) with the new energy equation from Step 4.

(400 units) = (L^(2a'))(M^(2b'))(T^(2c'))

**Step 6: Comparing Exponents**
By comparing the exponents of each fundamental unit on both sides of the equation, we can determine the relationship between the old and new energies.

For length:
a = 2a' => a' = a/2
For mass:
b = 2b' => b' = b/2
For time:
c = 2c' => c' = c/2

**Step 7: Substituting the Relationships**
Substituting the relationships obtained in Step 6 into the new energy equation from Step 4, we get:
(New Energy) = (L^(2(a/2)))(M^(2(b/2)))(T^(2(c/2)))

**Step 8: Simplifying the Equation**
Simplifying the above equation, we get:
(New Energy) = (L^a)(M^b)(T^c) = (400 units)

**Step 9: Conclusion**
From the above equation, it is clear that the magnitude of the energy in the new system will remain the same as the original energy, which is 400 units.

200 is answer