The average of 30 results is 20 and the average of other 20 results is 30. What is the average of all the results ?

Options

A. 24
B. 48
C. 25
D. 50

Answer

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

### Step 1: Calculate the sum of the first set of results
The average of the first 30 results is given as 20. The formula for average is:

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

From this, we can rearrange the formula to find the sum:

\[ \text{Sum of results} = \text{Average} \times \text{Number of results} \]

For the first set of results:

\[ \text{Sum of 30 results} = 20 \times 30 = 600 \]

### Step 2: Calculate the sum of the second set of results
The average of the second set of 20 results is given as 30. Using the same formula:

\[ \text{Sum of 20 results} = 30 \times 20 = 600 \]

### Step 3: Calculate the total sum of all results
Now, we need to find the total sum of all results by adding the sums of both sets:

\[ \text{Total sum} = \text{Sum of 30 results} + \text{Sum of 20 results} = 600 + 600 = 1200 \]

### Step 4: Calculate the total number of results
The total number of results is the sum of the number of results in both sets:

\[ \text{Total number of results} = 30 + 20 = 50 \]

### Step 5: Calculate the average of all results
Finally, we can find the average of all results using the total sum and the total number of results:

\[ \text{Average of all results} = \frac{\text{Total sum}}{\text{Total number of results}} = \frac{1200}{50} = 24 \]

Thus, the average of all the results is **24**.

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