Average of 40 results is 20. Average of 60 results is 30. What is the average of all the results?

Options

A. 32
B. 30
C. 26
D. 24

Answer

To find the average of all the results, we can follow these steps:

### Step 1: Calculate the sum of the first set of results.
Given that the average of 40 results is 20, we can calculate the sum of these results using the formula:
\[ \text{Sum} = \text{Average} \times \text{Number of results} \]
So,
\[ \text{Sum of first 40 results} = 20 \times 40 = 800 \]

### Step 2: Calculate the sum of the second set of results.
Next, we know that the average of 60 results is 30. We can calculate the sum of these results in the same way:
\[ \text{Sum of second 60 results} = 30 \times 60 = 1800 \]

### Step 3: Calculate the total sum of all results.
Now, we can find the total sum of all results by adding the sums from both sets:
\[ \text{Total Sum} = \text{Sum of first 40 results} + \text{Sum of second 60 results} \]
So,
\[ \text{Total Sum} = 800 + 1800 = 2600 \]

### Step 4: Calculate the total number of results.
Next, we need to find the total number of results:
\[ \text{Total Number of Results} = 40 + 60 = 100 \]

### Step 5: Calculate the average of all results.
Finally, we can find the average of all results using the formula:
\[ \text{Average} = \frac{\text{Total Sum}}{\text{Total Number of Results}} \]
So,
\[ \text{Average} = \frac{2600}{100} = 26 \]

Thus, the average of all the results is **26**.