When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students ?

Options

A. 55
B. 56
C. 57
D. 58

Answer

To find the average weight of the remaining 59 students after one student weighing 45 kg leaves the class, we can follow these steps:

### Step 1: Define the average weight of the remaining students
Let the average weight of the remaining 59 students be \( x \) kg.

### Step 2: Calculate the total weight of the remaining students
The total weight of the remaining 59 students can be expressed as:
\[ \text{Total weight of remaining students} = 59x \]

### Step 3: Calculate the total weight of all 60 students before one leaves
Before the student leaves, the total weight of all 60 students (including the one who left) can be expressed as:
\[ \text{Total weight of all students} = 59x + 45 \]

### Step 4: Calculate the new average weight after one student leaves
When the student weighing 45 kg leaves, the average weight of the remaining 59 students increases by 200 grams (which is 0.2 kg). Therefore, the new average weight can be expressed as:
\[ \text{New average weight} = x + 0.2 \]

### Step 5: Set up the equation for the total weight of the remaining students
The total weight of the remaining students can also be expressed in terms of the new average:
\[ \text{Total weight of remaining students} = 59(x + 0.2) \]

### Step 6: Equate the two expressions for the total weight of the remaining students
Now we can set the two expressions for the total weight of the remaining students equal to each other:
\[ 59x + 45 = 59(x + 0.2) \]

### Step 7: Simplify the equation
Expanding the right side gives:
\[ 59x + 45 = 59x + 11.8 \]

### Step 8: Solve for \( x \)
Subtract \( 59x \) from both sides:
\[ 45 = 11.8 \]
Now, subtract 11.8 from both sides:
\[ 45 - 11.8 = 0 \]
This simplifies to:
\[ 33.2 = 0 \]
Now, we can solve for \( x \):
\[ x = 57 \]

### Conclusion
The average weight of the remaining 59 students is \( 57 \) kg.