The mean weight of 60 students of a class is 52.75 kg. If the mean weight of 25 of them is 51 kg., find the mean weight of remaining students.

Options

A. 58 kg
B. 56 kg
C. 54 kg
D. 51 kg

Answer

To find the mean weight of the remaining students, we can follow these steps:

### Step 1: Calculate the total weight of all 60 students
The mean weight of 60 students is given as 52.75 kg.

To find the total weight, we use the formula:
\[ \text{Total Weight} = \text{Mean Weight} \times \text{Number of Students} \]
Substituting the values:
\[ \text{Total Weight} = 52.75 \, \text{kg} \times 60 = 3165 \, \text{kg} \]

### Step 2: Calculate the total weight of the 25 students
The mean weight of 25 students is given as 51 kg.

Using the same formula:
\[ \text{Total Weight of 25 Students} = 51 \, \text{kg} \times 25 = 1275 \, \text{kg} \]

### Step 3: Calculate the total weight of the remaining students
To find the total weight of the remaining students, we subtract the total weight of the 25 students from the total weight of all 60 students:
\[ \text{Total Weight of Remaining Students} = \text{Total Weight of 60 Students} - \text{Total Weight of 25 Students} \]
Substituting the values:
\[ \text{Total Weight of Remaining Students} = 3165 \, \text{kg} - 1275 \, \text{kg} = 1890 \, \text{kg} \]

### Step 4: Calculate the number of remaining students
The number of remaining students is:
\[ \text{Remaining Students} = 60 - 25 = 35 \]

### Step 5: Calculate the mean weight of the remaining students
Now, we can find the mean weight of the remaining 35 students using the formula:
\[ \text{Mean Weight of Remaining Students} = \frac{\text{Total Weight of Remaining Students}}{\text{Number of Remaining Students}} \]
Substituting the values:
\[ \text{Mean Weight of Remaining Students} = \frac{1890 \, \text{kg}}{35} = 54 \, \text{kg} \]

### Final Answer:
The mean weight of the remaining students is **54 kg**.

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