Average of 3 numbers is 9. If average of first two numbers be 12, then find the third number.

Options

A. 2
B. 3
C. 1
D. 4

Answer

To solve the problem step by step, we will use the information provided about the averages of the numbers.

### Step 1: Understand the given information
We know that the average of three numbers is 9. This means:
\[ \text{Average} = \frac{a + b + c}{3} = 9 \]
Where \(a\), \(b\), and \(c\) are the three numbers.

### Step 2: Calculate the sum of the three numbers
From the average, we can find the sum of the three numbers:
\[ a + b + c = 9 \times 3 = 27 \]

### Step 3: Understand the second piece of information
We are also given that the average of the first two numbers \(a\) and \(b\) is 12. This means:
\[ \text{Average} = \frac{a + b}{2} = 12 \]

### Step 4: Calculate the sum of the first two numbers
From this average, we can find the sum of the first two numbers:
\[ a + b = 12 \times 2 = 24 \]

### Step 5: Find the third number
Now, we can use the sums we calculated to find the third number \(c\):
\[ a + b + c = 27 \]
Substituting \(a + b = 24\) into the equation:
\[ 24 + c = 27 \]
Now, solve for \(c\):
\[ c = 27 - 24 = 3 \]

### Conclusion
The third number \(c\) is 3.