Given 1 + 2 + 3 + 4 + .... +10 = 55, then the sum 6 + 12 + 18 + 24 + ... + 60 is equal to :

Options

A. `300`
B. `655`
C. `330`
D. `455`

Answer

To solve the problem, we need to find the sum of the series 6 + 12 + 18 + 24 + ... + 60.

### Step-by-Step Solution:

1. **Identify the Series**: The series given is 6, 12, 18, 24, ..., 60. We can see that each term in this series is a multiple of 6.

2. **Factor out the Common Multiple**: We can factor out 6 from each term:
\[ 6 + 12 + 18 + 24 + ... + 60 = 6(1 + 2 + 3 + 4 + ... + 10) \]

3. **Identify the Inner Series**: The inner series is \(1 + 2 + 3 + 4 + ... + 10\). We know from the problem statement that this sum is equal to 55.

4. **Substitute the Known Sum**: We can substitute the known sum into our equation:
\[ 6(1 + 2 + 3 + 4 + ... + 10) = 6 \times 55 \]

5. **Calculate the Final Sum**: Now we calculate:
\[ 6 \times 55 = 330 \]

Thus, the sum of the series 6 + 12 + 18 + 24 + ... + 60 is **330**.

### Final Answer:
The sum is **330**.