The total number of students in sections A and B ofa class is 72. The ratio of the number of students in A and B is 7: 5. The average weight(in kg) of the students in section B is 20% more than that of the studentsin section A.If the average weight of all the students in the class is 52 kg, then whatis the average weight (in kg) of the students in section B?

Options

A. 58.2
B. 57.9
C. 57.6
D. 56.4

Answer

To solve the problem step by step, we will break down the information given and perform the necessary calculations.

### Step 1: Determine the number of students in sections A and B
The total number of students in sections A and B is 72, and the ratio of students in A to B is 7:5.

Let the number of students in section A be \(7x\) and in section B be \(5x\).

From the information given:
\[ 7x + 5x = 72 \]
\[ 12x = 72 \]
\[ x = \frac{72}{12} = 6 \]

Now, we can find the number of students in each section:
- Number of students in section A: \(7x = 7 \times 6 = 42\)
- Number of students in section B: \(5x = 5 \times 6 = 30\)

### Step 2: Set up the average weights
Let the average weight of students in section A be \(x\) kg. According to the problem, the average weight of students in section B is 20% more than that of section A. Therefore, we can express the average weight of section B as:
\[ \text{Average weight of B} = x + 0.2x = 1.2x \]

### Step 3: Calculate the overall average weight
The overall average weight of all students in the class is given as 52 kg. The formula for the combined average is:
\[ \text{Combined Average} = \frac{(n_A \cdot \text{Average A}) + (n_B \cdot \text{Average B})}{n_A + n_B} \]
Where:
- \(n_A = 42\) (number of students in A)
- \(n_B = 30\) (number of students in B)

Substituting the values into the formula:
\[ 52 = \frac{(42 \cdot x) + (30 \cdot 1.2x)}{42 + 30} \]
\[ 52 = \frac{42x + 36x}{72} \]
\[ 52 = \frac{78x}{72} \]

### Step 4: Solve for \(x\)
Cross-multiplying gives:
\[ 52 \cdot 72 = 78x \]
\[ 3744 = 78x \]
\[ x = \frac{3744}{78} = 48 \]

### Step 5: Calculate the average weight of students in section B
Now that we have \(x\), we can find the average weight of students in section B:
\[ \text{Average weight of B} = 1.2x = 1.2 \times 48 = 57.6 \text{ kg} \]

### Final Answer
The average weight of the students in section B is **57.6 kg**.

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