In each of the following questions a question is followed by information given in three statements. You have to study the question along with statements and decide the information given in which of the statement(s) is necessary and sufficient to answer the question.
What is the average weight of girls in the class?
Average weight of all the 60 student is 42 kg
Average weight of boys is 43 kg
Total weight of all the girls together is 1144 kg

Options

A. Any two of the three
B. All 1,2 and 3
C. 1 and 2 only
D. 2 and 3 only

Answer

To find the average weight of girls in the class, we can use the information provided in the statements. Let's break down the solution step by step.

### Step 1: Calculate the total weight of all students.
Given that the average weight of all 60 students is 42 kg, we can find the total weight of all students using the formula:

\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Students} \]

Substituting the values:

\[ \text{Total Weight} = 42 \, \text{kg} \times 60 = 2520 \, \text{kg} \]

### Step 2: Calculate the total weight of boys.
We know the average weight of boys is 43 kg. To find the total weight of boys, we first need to determine how many boys there are in the class.

Let \( b \) be the number of boys and \( g \) be the number of girls. Since there are a total of 60 students, we have:

\[ b + g = 60 \]

The total weight of boys can be expressed as:

\[ \text{Total Weight of Boys} = \text{Average Weight of Boys} \times \text{Number of Boys} = 43 \, \text{kg} \times b \]

### Step 3: Calculate the total weight of girls.
We are given that the total weight of all girls together is 1144 kg.

### Step 4: Set up the equation for total weight.
Now, we can set up the equation for the total weight of all students:

\[ \text{Total Weight of Boys} + \text{Total Weight of Girls} = \text{Total Weight of All Students} \]

Substituting the known values:

\[ 43b + 1144 = 2520 \]

### Step 5: Solve for the number of boys.
Rearranging the equation gives us:

\[ 43b = 2520 - 1144 \]
\[ 43b = 1376 \]
\[ b = \frac{1376}{43} = 32 \]

### Step 6: Calculate the number of girls.
Using the total number of students, we can find the number of girls:

\[ g = 60 - b = 60 - 32 = 28 \]

### Step 7: Calculate the average weight of girls.
Now that we have the total weight of girls (1144 kg) and the number of girls (28), we can calculate the average weight of girls:

\[ \text{Average Weight of Girls} = \frac{\text{Total Weight of Girls}}{\text{Number of Girls}} = \frac{1144 \, \text{kg}}{28} \]

Calculating this gives:

\[ \text{Average Weight of Girls} = 40.8 \, \text{kg} \]

### Final Answer:
The average weight of girls in the class is **40.8 kg**.

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