A class of 50 students belonging to the Kindergraten is divided in two sections A and B , having students in the ratio 2:3 respectively. The average weight of the students of the entire calss is 40 Ibs. The average weight of the students of section A is 2 Ibs . less than that of the students B. What is the average weight of the students of section B ?

Options

A. 32.6 Ibs.
B. 36.4 Ibs .
C. 38.8 Ibs.
D. 40.8 Ibs.

Answer

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

### Step 1: Determine the number of students in each section
The total number of students is 50, and they are divided in the ratio of 2:3 for sections A and B.

Let the number of students in section A be \(2x\) and in section B be \(3x\).

Since the total number of students is 50:
\[ 2x + 3x = 50 \]
\[ 5x = 50 \]
\[ x = 10 \]

Thus, the number of students in section A is:
\[ 2x = 2 \times 10 = 20 \]
And in section B:
\[ 3x = 3 \times 10 = 30 \]

### Step 2: Set up the average weights
Let the average weight of students in section B be \(x\) lbs. According to the problem, the average weight of students in section A is 2 lbs less than that of section B. Therefore, the average weight of students in section A is:
\[ x - 2 \text{ lbs} \]

### Step 3: Calculate the total weight of each section
The total weight of students in section A can be calculated as:
\[ \text{Total weight of A} = \text{Average weight of A} \times \text{Number of students in A} = (x - 2) \times 20 \]
The total weight of students in section B is:
\[ \text{Total weight of B} = \text{Average weight of B} \times \text{Number of students in B} = x \times 30 \]

### Step 4: Set up the equation for total weight
The total weight of the entire class is the sum of the weights of sections A and B. The average weight of the entire class is given as 40 lbs, so the total weight is:
\[ \text{Total weight} = 50 \times 40 = 2000 \text{ lbs} \]

Now we can set up the equation:
\[ 20(x - 2) + 30x = 2000 \]

### Step 5: Simplify and solve the equation
Expanding the equation:
\[ 20x - 40 + 30x = 2000 \]
Combining like terms:
\[ 50x - 40 = 2000 \]
Adding 40 to both sides:
\[ 50x = 2040 \]
Dividing by 50:
\[ x = \frac{2040}{50} = 40.8 \]

### Step 6: Conclusion
The average weight of the students in section B is:
\[ \boxed{40.8 \text{ lbs}} \]

---