The average weight of students in a class was 60.5 kg. When & students, whose average weight was 65 kg, joined the class, then the average weight of all the students increased by 0.9 kg. The total number of students now in the class is:

Options

A. 35
B. 40
C. 32
D. 27

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let \( n \) be the initial number of students in the class. The average weight of these students is given as 60.5 kg.

### Step 2: Calculate the Total Weight of Initial Students
The total weight of the initial \( n \) students can be calculated as:
\[ \text{Total weight of initial students} = 60.5n \]

### Step 3: Calculate the Total Weight of New Students
When 8 new students join the class with an average weight of 65 kg, the total weight of these new students is:
\[ \text{Total weight of new students} = 65 \times 8 = 520 \text{ kg} \]

### Step 4: Calculate the New Total Weight
The new total weight of all students in the class after the 8 new students join is:
\[ \text{New total weight} = 60.5n + 520 \]

### Step 5: Calculate the New Average Weight
After the 8 new students join, the total number of students becomes \( n + 8 \). The new average weight is given as:
\[ \text{New average weight} = 60.5 + 0.9 = 61.4 \text{ kg} \]

### Step 6: Set Up the Equation for the New Average Weight
We can set up the equation for the new average weight:
\[ \frac{60.5n + 520}{n + 8} = 61.4 \]

### Step 7: Cross Multiply to Eliminate the Fraction
Cross multiplying gives us:
\[ 60.5n + 520 = 61.4(n + 8) \]

### Step 8: Expand the Right Side
Expanding the right side of the equation:
\[ 60.5n + 520 = 61.4n + 491.2 \]

### Step 9: Rearrange the Equation
Rearranging the equation to isolate \( n \):
\[ 60.5n - 61.4n = 491.2 - 520 \]
\[ -0.9n = -28.8 \]

### Step 10: Solve for \( n \)
Dividing both sides by -0.9 gives:
\[ n = \frac{28.8}{0.9} = 32 \]

### Step 11: Calculate the Total Number of Students
The total number of students now in the class is:
\[ n + 8 = 32 + 8 = 40 \]

### Final Answer
The total number of students now in the class is **40**.