Divide 1224 into three parts such that first part be double that of second part and second part be `1/3` of the third part.

Answer

To solve the problem of dividing 1224 into three parts where the first part is double that of the second part and the second part is one-third of the third part, we can follow these steps:

### Step 1: Define the Parts
Let:
- The second part be \( B \).
- The first part \( A \) is double that of the second part, so \( A = 2B \).
- The third part \( C \) is three times the second part, so \( C = 3B \).

### Step 2: Set Up the Equation
According to the problem, the sum of the three parts equals 1224:
\[ A + B + C = 1224 \]
Substituting the expressions for \( A \) and \( C \):
\[ 2B + B + 3B = 1224 \]

### Step 3: Combine Like Terms
Combine the terms on the left side:
\[ 6B = 1224 \]

### Step 4: Solve for \( B \)
Now, divide both sides by 6 to find \( B \):
\[ B = \frac{1224}{6} = 204 \]

### Step 5: Calculate \( A \) and \( C \)
Now that we have \( B \), we can find \( A \) and \( C \):
- For \( A \):
\[ A = 2B = 2 \times 204 = 408 \]
- For \( C \):
\[ C = 3B = 3 \times 204 = 612 \]

### Step 6: Final Parts
Thus, the three parts are:
- First part \( A = 408 \)
- Second part \( B = 204 \)
- Third part \( C = 612 \)

### Summary of the Parts
The three parts are:
- \( A = 408 \)
- \( B = 204 \)
- \( C = 612 \)