The average of 9 numbers is 19. If the average of the first four numbers is 14, then the average of the last 5 numbers is:

Options

A. 20
B. 10
C. 25.25
D. 23

Answer

To solve the problem step by step, we will use the information given about the averages to find the average of the last five numbers.

### Step 1: Find the total sum of the 9 numbers
The average of 9 numbers is given as 19.
To find the total sum (S) of these 9 numbers, we use the formula for average:

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

So, we can rearrange this to find the sum:

\[ S = \text{Average} \times \text{Number of numbers} = 19 \times 9 = 171 \]

### Step 2: Find the total sum of the first 4 numbers
The average of the first 4 numbers is given as 14.
Using the same formula for average, we can find the sum of the first 4 numbers (S1):

\[ S1 = \text{Average} \times \text{Number of numbers} = 14 \times 4 = 56 \]

### Step 3: Find the total sum of the last 5 numbers
Now, we need to find the sum of the last 5 numbers (S2). We know that the total sum of all 9 numbers is the sum of the first 4 numbers and the last 5 numbers:

\[ S = S1 + S2 \]

Substituting the values we have:

\[ 171 = 56 + S2 \]

To find S2, we rearrange the equation:

\[ S2 = 171 - 56 = 115 \]

### Step 4: Find the average of the last 5 numbers
Finally, we can find the average of the last 5 numbers (A2) using the sum we just calculated:

\[ A2 = \frac{S2}{\text{Number of last numbers}} = \frac{115}{5} = 23 \]

Thus, the average of the last 5 numbers is **23**.

### Summary of Steps:
1. Calculate the total sum of the 9 numbers using the average.
2. Calculate the total sum of the first 4 numbers using their average.
3. Subtract the sum of the first 4 numbers from the total sum to find the sum of the last 5 numbers.
4. Divide the sum of the last 5 numbers by 5 to find their average.