The average weight of 20 students in a class is increased by 0.75 kg when one of the students weighing 30 kg is replaced by a new student. Weight of the new student (in kg) is :

Options

A. 35
B. 40
C. 45
D. 50

Answer

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

### Step 1: Understand the problem
We know that the average weight of 20 students increases by 0.75 kg when a student weighing 30 kg is replaced by a new student. We need to find the weight of the new student.

### Step 2: Calculate the total increase in weight
The total increase in weight due to the average increase can be calculated using the formula:
\[ \text{Total Increase} = \text{Number of Students} \times \text{Increase in Average} \]
Here, the number of students is 20 and the increase in average is 0.75 kg.

\[ \text{Total Increase} = 20 \times 0.75 = 15 \text{ kg} \]

### Step 3: Determine the weight change
When the student weighing 30 kg is replaced, the total weight of the class increases by 15 kg. This means that the new student must weigh more than the student being replaced.

### Step 4: Set up the equation
Let \( x \) be the weight of the new student. The total weight change can be expressed as:
\[ \text{Weight of New Student} - \text{Weight of Replaced Student} = \text{Total Increase} \]
Substituting the known values:
\[ x - 30 = 15 \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = 15 + 30 \]
\[ x = 45 \text{ kg} \]

### Conclusion
The weight of the new student is 45 kg.

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