Average weight of P and Q is 32 kg. Average weight of Q and R is 43 kg. Average weight of P and R is 51 kg. What is the average weight (in kg) of P, Q and R?

Options

A. A)44
B. B)42
C. C)40
D. D)38

Answer

To find the average weight of P, Q, and R, we can follow these steps:

1. **Calculate the total weight of P and Q**:
Given that the average weight of P and Q is 32 kg, we can express this as:
\[ \frac{P + Q}{2} = 32 \]
Multiplying both sides by 2 gives:
\[ P + Q = 64 \quad \text{(1)} \]

2. **Calculate the total weight of Q and R**:
Given that the average weight of Q and R is 43 kg, we can express this as:
\[ \frac{Q + R}{2} = 43 \]
Multiplying both sides by 2 gives:
\[ Q + R = 86 \quad \text{(2)} \]

3. **Calculate the total weight of P and R**:
Given that the average weight of P and R is 51 kg, we can express this as:
\[ \frac{P + R}{2} = 51 \]
Multiplying both sides by 2 gives:
\[ P + R = 102 \quad \text{(3)} \]

4. **Add all three equations**:
Now, we can add equations (1), (2), and (3):
\[ (P + Q) + (Q + R) + (P + R) = 64 + 86 + 102 \]
This simplifies to:
\[ 2P + 2Q + 2R = 252 \]

5. **Divide by 2 to find the total weight of P, Q, and R**:
\[ P + Q + R = \frac{252}{2} = 126 \quad \text{(4)} \]

6. **Calculate the average weight of P, Q, and R**:
To find the average weight, we divide the total weight by 3:
\[ \text{Average} = \frac{P + Q + R}{3} = \frac{126}{3} = 42 \text{ kg} \]

Thus, the average weight of P, Q, and R is **42 kg**.