The average weight of A,B and C is 65 kg. If the average weight of A and B is 63.5 kg, and the average weight of A and C is 67.5 kg , then the weight of A (in kg) is :

Options

A. 67
B. 65
C. 68
D. 60

Answer

To find the weight of A, we can follow these steps:

### Step 1: Calculate the total weight of A, B, and C
The average weight of A, B, and C is given as 65 kg. Since there are three individuals, we can calculate the total weight as follows:

\[ \text{Total weight of A, B, and C} = \text{Average} \times \text{Number of individuals} = 65 \times 3 = 195 \text{ kg} \]

### Step 2: Calculate the total weight of A and B
The average weight of A and B is given as 63.5 kg. Therefore, we can calculate their total weight:

\[ \text{Total weight of A and B} = \text{Average} \times \text{Number of individuals} = 63.5 \times 2 = 127 \text{ kg} \]

### Step 3: Calculate the weight of C
Now, we can find the weight of C by subtracting the total weight of A and B from the total weight of A, B, and C:

\[ \text{Weight of C} = \text{Total weight of A, B, and C} - \text{Total weight of A and B} = 195 - 127 = 68 \text{ kg} \]

### Step 4: Calculate the total weight of A and C
The average weight of A and C is given as 67.5 kg. Thus, we can calculate their total weight:

\[ \text{Total weight of A and C} = \text{Average} \times \text{Number of individuals} = 67.5 \times 2 = 135 \text{ kg} \]

### Step 5: Calculate the weight of A
Now, we can find the weight of A by using the total weight of A and C and subtracting the weight of C:

\[ \text{Weight of A} = \text{Total weight of A and C} - \text{Weight of C} = 135 - 68 = 67 \text{ kg} \]

### Final Answer
The weight of A is **67 kg**.

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