Average of 31 numbers is 19. If the average of first 8 numbers is 24, then what is the average of the remaining numbers?

Options

A. 17.26
B. 23.25
C. 26.2
D. 25.45

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the sum of 31 numbers
The average of 31 numbers is given as 19. The formula for average is:

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

Using this formula, we can find the sum of the 31 numbers:

\[ 19 = \frac{\text{Sum of 31 numbers}}{31} \]

To find the sum of 31 numbers, we multiply both sides by 31:

\[ \text{Sum of 31 numbers} = 19 \times 31 = 589 \]

### Step 2: Calculate the sum of the first 8 numbers
The average of the first 8 numbers is given as 24. We can use the same formula to find the sum of these 8 numbers:

\[ 24 = \frac{\text{Sum of first 8 numbers}}{8} \]

Multiplying both sides by 8 gives us:

\[ \text{Sum of first 8 numbers} = 24 \times 8 = 192 \]

### Step 3: Calculate the sum of the remaining numbers
Now, we can find the sum of the remaining numbers by subtracting the sum of the first 8 numbers from the sum of all 31 numbers:

\[ \text{Sum of remaining numbers} = \text{Sum of 31 numbers} - \text{Sum of first 8 numbers} \]

Substituting the values we calculated:

\[ \text{Sum of remaining numbers} = 589 - 192 = 397 \]

### Step 4: Calculate the average of the remaining numbers
There are 31 numbers in total, and we have already accounted for 8 of them. Therefore, the number of remaining numbers is:

\[ 31 - 8 = 23 \]

Now, we can find the average of the remaining numbers:

\[ \text{Average of remaining numbers} = \frac{\text{Sum of remaining numbers}}{\text{Number of remaining numbers}} = \frac{397}{23} \]

Calculating this gives:

\[ \text{Average of remaining numbers} \approx 17.26 \]

### Final Answer
Thus, the average of the remaining numbers is approximately **17.26**.

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