The mean weight of 25 students of a class is 52 kg. if the mean weight of the first 13 student of the class is 48 kg and that of the last 13 students is 55kg , find the weight of the 13th student.

Answer

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

### Step 1: Calculate the total weight of all 25 students.
The mean weight of the 25 students is given as 52 kg. To find the total weight, we multiply the mean by the number of students.

\[ \text{Total weight of 25 students} = \text{Mean} \times \text{Number of students} = 52 \, \text{kg} \times 25 = 1300 \, \text{kg} \]

### Step 2: Calculate the total weight of the first 13 students.
The mean weight of the first 13 students is given as 48 kg. We can find their total weight similarly.

\[ \text{Total weight of first 13 students} = 48 \, \text{kg} \times 13 = 624 \, \text{kg} \]

### Step 3: Calculate the total weight of the last 13 students.
The mean weight of the last 13 students is given as 55 kg. We calculate their total weight as follows:

\[ \text{Total weight of last 13 students} = 55 \, \text{kg} \times 13 = 715 \, \text{kg} \]

### Step 4: Set up the equation to find the weight of the 13th student.
Since the 13th student is counted in both the first 13 and the last 13 students, we need to account for this overlap. Let's denote the weight of the 13th student as \( x \).

The total weight of the first 13 students plus the total weight of the last 13 students minus the weight of the 13th student should equal the total weight of all 25 students:

\[ 624 + 715 - x = 1300 \]

### Step 5: Solve for \( x \).
Now, we can simplify the equation:

\[ 1339 - x = 1300 \]

To isolate \( x \), we subtract 1300 from both sides:

\[ 1339 - 1300 = x \]

\[ x = 39 \, \text{kg} \]

### Conclusion:
The weight of the 13th student is **39 kg**.

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