Divide 3740 in three parts in such a way that half of the first part, one - third of the second part and one-sixth of the third part are equal.
A. 700,1000,2040
B. 340,1360,2040
C. 680, 1020, 2040
D. 500, 1200, 2040

Options

A. D
B. B
C. A
D. C

Answer

To solve the problem of dividing 3740 into three parts such that half of the first part, one-third of the second part, and one-sixth of the third part are equal, follow these steps:

### Step 1: Define the Parts
Let the three parts be:
- First part = \( x \)
- Second part = \( y \)
- Third part = \( z \)

### Step 2: Set Up the Equation
According to the problem, we have:
\[ \frac{x}{2} = \frac{y}{3} = \frac{z}{6} \]
Let this common value be \( k \). Therefore, we can express \( x \), \( y \), and \( z \) in terms of \( k \):
- \( x = 2k \)
- \( y = 3k \)
- \( z = 6k \)

### Step 3: Write the Total Sum Equation
Since the total of the three parts is 3740, we can write:
\[ x + y + z = 3740 \]
Substituting the expressions for \( x \), \( y \), and \( z \):
\[ 2k + 3k + 6k = 3740 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ 11k = 3740 \]

### Step 5: Solve for \( k \)
Now, solve for \( k \):
\[ k = \frac{3740}{11} = 340 \]

### Step 6: Find Each Part
Now that we have \( k \), we can find each part:
- First part \( x = 2k = 2 \times 340 = 680 \)
- Second part \( y = 3k = 3 \times 340 = 1020 \)
- Third part \( z = 6k = 6 \times 340 = 2040 \)

### Step 7: State the Parts
Thus, the three parts are:
- First part: 680
- Second part: 1020
- Third part: 2040

### Conclusion
The correct answer is:
**C. 680, 1020, 2040**

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