Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements sufficient to answer the question. Read both the statements and give answer:
What is the total number of students (male and female) in the class?
I. The average weight of the students of the class is 60.4 kg. The average weight of male students is 64.2 kg and the average weight of female students is 54.7 kg.
II. The difference between number of male students and number of female students in the class is 10.

Options

A. if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C. if the data in statement I alone or in statement II alone are sufficient to answer the question.
D. if the data in both the statements I and II together are sufficient to answer the question.

Answer

To determine the total number of students (male and female) in the class, we will analyze the information provided in both statements step by step.

### Step 1: Analyze Statement I
- **Statement I** provides the average weights:
- Average weight of all students = 60.4 kg
- Average weight of male students = 64.2 kg
- Average weight of female students = 54.7 kg

Let:
- \( x \) = number of male students
- \( y \) = number of female students

From the average weight formula, we can set up the following equation based on the total weight:
\[ \frac{(64.2x + 54.7y)}{(x + y)} = 60.4 \]
Multiplying both sides by \( (x + y) \):
\[ 64.2x + 54.7y = 60.4(x + y) \]
Expanding the right side:
\[ 64.2x + 54.7y = 60.4x + 60.4y \]
Rearranging gives:
\[ 64.2x - 60.4x = 60.4y - 54.7y \]
\[ 3.8x = 5.7y \]
This gives us a relationship between \( x \) and \( y \), but we still have two unknowns and only one equation. Therefore, **Statement I alone is not sufficient** to determine the total number of students.

### Step 2: Analyze Statement II
- **Statement II** states that the difference between the number of male and female students is 10:
\[ x - y = 10 \]
This is a single equation with two unknowns. Thus, **Statement II alone is also not sufficient** to determine the total number of students.

### Step 3: Combine Statements I and II
Now, we combine both statements:
1. From Statement I: \( 3.8x = 5.7y \)
2. From Statement II: \( x - y = 10 \)

We can solve these two equations simultaneously.

From Statement II, we can express \( x \) in terms of \( y \):
\[ x = y + 10 \]

Substituting this into the equation from Statement I:
\[ 3.8(y + 10) = 5.7y \]
Expanding this gives:
\[ 3.8y + 38 = 5.7y \]
Rearranging gives:
\[ 38 = 5.7y - 3.8y \]
\[ 38 = 1.9y \]
\[ y = \frac{38}{1.9} = 20 \]

Now substituting \( y \) back into the equation for \( x \):
\[ x = y + 10 = 20 + 10 = 30 \]

### Step 4: Calculate Total Number of Students
Now we can find the total number of students:
\[ x + y = 30 + 20 = 50 \]

### Conclusion
Thus, the total number of students in the class is **50**.