The average weight of students in a class is 58.5 kg. Four more students having weights 49 kg, 51 kg, 54 kg and 68 kg join the class. Now the average weight of all the students in the class is 58.3 kg. The number of students in the class, initially was,

Options

A. 46
B. 54
C. 56
D. 44

Answer

To solve the problem step by step, we will follow the mathematical approach to find the initial number of students in the class.

### Step-by-Step Solution:

1. **Let the initial number of students be \( x \)**:
- We denote the initial number of students in the class as \( x \).

2. **Calculate the total weight of the initial students**:
- The average weight of the students is given as 58.5 kg.
- Therefore, the total weight of these \( x \) students can be calculated as:
\[ \text{Total weight} = \text{Average weight} \times \text{Number of students} = 58.5 \times x \]

3. **Add the weights of the new students**:
- Four new students join the class with weights 49 kg, 51 kg, 54 kg, and 68 kg.
- The total weight of the new students is:
\[ 49 + 51 + 54 + 68 = 222 \text{ kg} \]

4. **Calculate the new total weight**:
- The new total weight after adding the four students becomes:
\[ \text{New total weight} = 58.5x + 222 \]

5. **Calculate the new average weight**:
- The new average weight of the students is given as 58.3 kg.
- The total number of students after the new students join is \( x + 4 \).
- The equation for the new average weight can be set up as:
\[ \frac{58.5x + 222}{x + 4} = 58.3 \]

6. **Cross-multiply to eliminate the fraction**:
- Cross-multiplying gives:
\[ 58.5x + 222 = 58.3(x + 4) \]

7. **Expand the right side**:
- Expanding the right side:
\[ 58.5x + 222 = 58.3x + 233.2 \]

8. **Rearranging the equation**:
- Now, we will collect like terms:
\[ 58.5x - 58.3x = 233.2 - 222 \]
\[ 0.2x = 11.2 \]

9. **Solve for \( x \)**:
- Dividing both sides by 0.2 gives:
\[ x = \frac{11.2}{0.2} = 56 \]

10. **Conclusion**:
- The initial number of students in the class was \( \boxed{56} \).