The total number of students in class A and B is 92. The number of students in A is 30% more than that in B. The average weight (in kg) of students in B is 50% more than that of students in A. If the average weight of all the students in A and B is 56 kg, then what is the average weight (in kg) of students in B ?

Options

A. 46
B. 40
C. 69
D. 52

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Define Variables
Let the number of students in class B be \( b \). Since the number of students in class A is 30% more than in class B, we can express the number of students in class A as:
\[ a = b + 0.3b = 1.3b \]

### Step 2: Set Up the Equation for Total Students
The total number of students in classes A and B is given as 92. Therefore, we can write the equation:
\[ a + b = 92 \]
Substituting \( a = 1.3b \) into the equation gives:
\[ 1.3b + b = 92 \]
\[ 2.3b = 92 \]

### Step 3: Solve for \( b \)
Now, we can solve for \( b \):
\[ b = \frac{92}{2.3} = 40 \]
Thus, the number of students in class B is 40.

### Step 4: Calculate the Number of Students in Class A
Using the value of \( b \):
\[ a = 1.3b = 1.3 \times 40 = 52 \]
So, the number of students in class A is 52.

### Step 5: Define Average Weights
Let the average weight of students in class A be \( x \). According to the problem, the average weight of students in class B is 50% more than that of students in class A, which can be expressed as:
\[ \text{Average weight of B} = x + 0.5x = 1.5x \]

### Step 6: Set Up the Equation for Average Weight
The average weight of all students in classes A and B combined is given as 56 kg. The total weight can be expressed as:
\[ \text{Total weight} = (a \cdot \text{Average weight of A}) + (b \cdot \text{Average weight of B}) \]
Substituting the values we have:
\[ \text{Total weight} = (52 \cdot x) + (40 \cdot 1.5x) \]
This simplifies to:
\[ \text{Total weight} = 52x + 60x = 112x \]

### Step 7: Set Up the Equation for Average Weight
The average weight of all students is given by:
\[ \frac{\text{Total weight}}{\text{Total number of students}} = 56 \]
Substituting the total weight and the total number of students:
\[ \frac{112x}{92} = 56 \]

### Step 8: Solve for \( x \)
Cross-multiplying gives:
\[ 112x = 56 \times 92 \]
Calculating \( 56 \times 92 \):
\[ 56 \times 92 = 5152 \]
Thus:
\[ 112x = 5152 \]
Now, solving for \( x \):
\[ x = \frac{5152}{112} = 46 \]

### Step 9: Calculate Average Weight of Students in Class B
Now, we can find the average weight of students in class B:
\[ \text{Average weight of B} = 1.5x = 1.5 \times 46 = 69 \]

### Final Answer
The average weight of students in class B is:
\[ \boxed{69 \text{ kg}} \]