Out of six consecutive natural numbers, if the sum of first three is 27, what is the sum of the other three ?

Options

A. 36
B. 35
C. 25
D. 24

Answer

To solve the problem step by step, we will first define the six consecutive natural numbers and then find the sum of the last three based on the information given.

### Step 1: Define the six consecutive natural numbers
Let the six consecutive natural numbers be:
- \( n, n+1, n+2, n+3, n+4, n+5 \)

### Step 2: Find the sum of the first three numbers
The first three numbers are:
- \( n, n+1, n+2 \)

The sum of these three numbers is:
\[ n + (n + 1) + (n + 2) = 3n + 3 \]

### Step 3: Set the equation for the sum of the first three numbers
According to the problem, the sum of the first three numbers is given as 27. Therefore, we can set up the equation:
\[ 3n + 3 = 27 \]

### Step 4: Solve for \( n \)
To solve for \( n \), we will first subtract 3 from both sides:
\[ 3n = 27 - 3 \]
\[ 3n = 24 \]
Now, divide by 3:
\[ n = \frac{24}{3} = 8 \]

### Step 5: Identify the six consecutive numbers
Now that we have \( n = 8 \), we can identify the six consecutive natural numbers:
- \( 8, 9, 10, 11, 12, 13 \)

### Step 6: Find the sum of the last three numbers
The last three numbers are:
- \( 10, 11, 12, 13 \)

Now, we will calculate their sum:
\[ 10 + 11 + 12 + 13 = 11 + 12 + 13 = 36 \]

### Conclusion
Thus, the sum of the last three consecutive natural numbers is:
\[ \text{Sum of the last three numbers} = 36 \]