The average of 60 student’s results is 38. If the average of the first 22 students is 36, and that of the last 32 students is 32, then the average result of the remaining students is:

Options

A. `77.33`
B. `81.9`
C. `65.30`
D. `52.12`

Answer

To solve the problem step by step, we will follow the given information and calculate the average of the remaining students.

### Step 1: Calculate the total marks of all 60 students.
Given that the average of 60 students is 38, we can calculate the total marks as follows:

\[ \text{Total marks of 60 students} = \text{Average} \times \text{Number of students} = 38 \times 60 = 2280 \]

### Step 2: Calculate the total marks of the first 22 students.
The average of the first 22 students is given as 36. Thus, the total marks for these students can be calculated as:

\[ \text{Total marks of first 22 students} = 36 \times 22 = 792 \]

### Step 3: Calculate the total marks of the last 32 students.
The average of the last 32 students is given as 32. Therefore, the total marks for these students can be calculated as:

\[ \text{Total marks of last 32 students} = 32 \times 32 = 1024 \]

### Step 4: Calculate the total marks of the remaining students.
Now, we can find the total marks of the remaining students by subtracting the total marks of the first 22 and last 32 students from the total marks of all 60 students:

\[ \text{Total marks of remaining students} = \text{Total marks of 60 students} - (\text{Total marks of first 22 students} + \text{Total marks of last 32 students}) \]

Substituting the values we calculated:

\[ \text{Total marks of remaining students} = 2280 - (792 + 1024) = 2280 - 1816 = 464 \]

### Step 5: Calculate the number of remaining students.
The number of remaining students can be calculated as:

\[ \text{Number of remaining students} = 60 - (22 + 32) = 60 - 54 = 6 \]

### Step 6: Calculate the average of the remaining students.
Finally, we can find the average of the remaining students by dividing the total marks of the remaining students by the number of remaining students:

\[ \text{Average of remaining students} = \frac{\text{Total marks of remaining students}}{\text{Number of remaining students}} = \frac{464}{6} \approx 77.33 \]

Thus, the average result of the remaining students is approximately **77.33**.

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