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 given about the averages of the numbers.

### Step 1: Understand the average of three numbers.
The average of three numbers \( a, b, c \) is given as 9. The formula for the average is:

\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of observations}} \]

So, we can express this as:

\[ \frac{a + b + c}{3} = 9 \]

### Step 2: Calculate the sum of the three numbers.
To find the sum of the three numbers \( a + b + c \), we can rearrange the equation:

\[ a + b + c = 9 \times 3 = 27 \]

### Step 3: Understand the average of the first two numbers.
We are also given that the average of the first two numbers \( a \) and \( b \) is 12. Using the same average formula, we have:

\[ \frac{a + b}{2} = 12 \]

### Step 4: Calculate the sum of the first two numbers.
Now, we can find the sum of the first two numbers \( a + b \):

\[ a + b = 12 \times 2 = 24 \]

### Step 5: Find the third number.
Now, we have the sum of all three numbers \( a + b + c = 27 \) and the sum of the first two numbers \( a + b = 24 \). We can find the third number \( c \) by subtracting the sum of the first two numbers from the total sum:

\[ c = (a + b + c) - (a + b) = 27 - 24 = 3 \]

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

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