To solve the problem step by step, we will use the information given about the average weights of A, B, and C.
### Step 1: Calculate the total weight of A, B, and C
The average weight of A, B, and C is given as 45 kg.
To find the total weight of A, B, and C, we can use the formula for average:
\[
\text{Average} = \frac{\text{Total Weight}}{\text{Number of Items}}
\]
So,
\[
\text{Total Weight of A, B, and C} = \text{Average} \times \text{Number of Items} = 45 \times 3 = 135 \text{ kg}
\]
### Step 2: Calculate the total weight of A and B
The average weight of A and B is given as 40 kg.
Using the same formula:
\[
\text{Total Weight of A and B} = \text{Average} \times \text{Number of Items} = 40 \times 2 = 80 \text{ kg}
\]
### Step 3: Calculate the weight of C
We know the total weight of A, B, and C is 135 kg and the total weight of A and B is 80 kg.
To find the weight of C, we subtract the total weight of A and B from the total weight of A, B, and C:
\[
\text{Weight of C} = \text{Total Weight of A, B, and C} - \text{Total Weight of A and B} = 135 - 80 = 55 \text{ kg}
\]
### Step 4: Calculate the total weight of B and C
The average weight of B and C is given as 43 kg.
Using the formula again:
\[
\text{Total Weight of B and C} = \text{Average} \times \text{Number of Items} = 43 \times 2 = 86 \text{ kg}
\]
### Step 5: Calculate the weight of B
Now we have the total weight of A, B, and C (135 kg) and the total weight of B and C (86 kg).
To find the weight of A, we can subtract the total weight of B and C from the total weight of A, B, and C:
\[
\text{Weight of A} = \text{Total Weight of A, B, and C} - \text{Total Weight of B and C} = 135 - 86 = 49 \text{ kg}
\]
### Step 6: Calculate the weight of B
Now we know the weight of A (49 kg) and C (55 kg). We can find the weight of B using the total weight of A, B, and C:
\[
\text{Weight of B} = \text{Total Weight of A, B, and C} - \text{Weight of A} - \text{Weight of C} = 135 - 49 - 55
\]
Calculating this gives:
\[
\text{Weight of B} = 135 - 104 = 31 \text{ kg}
\]
### Final Answer
The weight of B is **31 kg**.
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