There are 3 students in a group. If the weight of any student is added to the average weight of the other two, the sums received are 48 kg, 52 kg and 59 kg. The average weight (in kg) of the three students is:

Options

A. A)27
B. B)`26.5`
C. C)`27.5`
D. D)28

Answer

To find the average weight of the three students, we can follow these steps:

### Step 1: Define the variables
Let the weights of the three students be A, B, and C.

### Step 2: Set up the equations
According to the problem, we have the following equations based on the information given:
1. When A's weight is added to the average weight of B and C:
\[ A + \frac{B + C}{2} = 48 \quad \text{(Equation 1)} \]
2. When B's weight is added to the average weight of A and C:
\[ B + \frac{A + C}{2} = 52 \quad \text{(Equation 2)} \]
3. When C's weight is added to the average weight of A and B:
\[ C + \frac{A + B}{2} = 59 \quad \text{(Equation 3)} \]

### Step 3: Simplify the equations
We can rewrite these equations to eliminate the fractions:
1. From Equation 1:
\[ 2A + B + C = 96 \quad \text{(Multiply by 2)} \]
2. From Equation 2:
\[ 2B + A + C = 104 \quad \text{(Multiply by 2)} \]
3. From Equation 3:
\[ 2C + A + B = 118 \quad \text{(Multiply by 2)} \]

### Step 4: Add the equations together
Now, we add all three simplified equations:
\[ (2A + B + C) + (2B + A + C) + (2C + A + B) = 96 + 104 + 118 \]
This simplifies to:
\[ 4A + 4B + 4C = 318 \]

### Step 5: Solve for A + B + C
Dividing both sides by 4 gives:
\[ A + B + C = \frac{318}{4} = 79.5 \quad \text{(Equation 4)} \]

### Step 6: Calculate the average weight
To find the average weight of the three students, we divide the total weight by 3:
\[ \text{Average weight} = \frac{A + B + C}{3} = \frac{79.5}{3} = 26.5 \text{ kg} \]

### Conclusion
Thus, the average weight of the three students is **26.5 kg**.

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