The average weight of A B and C Is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight (in kg) of B is

Options

A. 20
B. 26
C. 31
D. 17

Answer

To solve the problem step by step, we will use the information given about the average weights of A, B, and C.

### Step-by-Step Solution:

1. **Calculate the total weight of A, B, and C:**
- The average weight of A, B, and C is given as 45 kg.
- Since there are 3 individuals (A, B, and C), we can calculate the total weight using the formula for average:
\[ \text{Total weight} = \text{Average} \times \text{Number of individuals} \]
\[ A + B + C = 45 \times 3 = 135 \text{ kg} \]

2. **Calculate the total weight of A and B:**
- The average weight of A and B is given as 40 kg.
- Since there are 2 individuals (A and B), we can calculate their total weight:
\[ A + B = 40 \times 2 = 80 \text{ kg} \]

3. **Calculate the total weight of B and C:**
- The average weight of B and C is given as 43 kg.
- Since there are 2 individuals (B and C), we can calculate their total weight:
\[ B + C = 43 \times 2 = 86 \text{ kg} \]

4. **Set up the equations:**
- Now we have three equations:
1. \( A + B + C = 135 \) (Equation 1)
2. \( A + B = 80 \) (Equation 2)
3. \( B + C = 86 \) (Equation 3)

5. **Find the weight of C:**
- To find C, we can subtract Equation 2 from Equation 1:
\[ C = (A + B + C) - (A + B) = 135 - 80 = 55 \text{ kg} \]

6. **Find the weight of B:**
- Now that we have the weight of C, we can substitute it back into Equation 3 to find B:
\[ B + C = 86 \]
\[ B + 55 = 86 \]
\[ B = 86 - 55 = 31 \text{ kg} \]

### Final Answer:
The weight of B is **31 kg**.

---