The average weight of 8 men is increased by 2 kg when one of the men whose weight is 50kg is replaced by a new man the weight of the new man is

Options

A. 52 kg
B. 58kg
C. 66 kg
D. 68kg

Answer

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

### Step 1: Calculate the total weight of the 8 men before the replacement.
Let the average weight of the 8 men be \( x \) kg. Therefore, the total weight of the 8 men is:
\[ \text{Total weight} = 8x \]

### Step 2: Determine the new average weight after the replacement.
According to the problem, the average weight increases by 2 kg when one man is replaced. Therefore, the new average weight is:
\[ \text{New average weight} = x + 2 \]

### Step 3: Calculate the total weight of the 8 men after the replacement.
The total weight of the 8 men after the replacement becomes:
\[ \text{New total weight} = 8(x + 2) = 8x + 16 \]

### Step 4: Set up the equation for the total weight before and after the replacement.
When one man weighing 50 kg is replaced by the new man, the total weight after the replacement can also be expressed as:
\[ \text{New total weight} = \text{Old total weight} - \text{Weight of the man replaced} + \text{Weight of the new man} \]
Substituting the known values:
\[ 8x + 16 = 8x - 50 + \text{Weight of the new man} \]

### Step 5: Simplify the equation to find the weight of the new man.
Now, we can simplify the equation:
\[ 8x + 16 = 8x - 50 + \text{Weight of the new man} \]
Subtract \( 8x \) from both sides:
\[ 16 = -50 + \text{Weight of the new man} \]
Now, add 50 to both sides:
\[ \text{Weight of the new man} = 16 + 50 = 66 \text{ kg} \]

### Conclusion
The weight of the new man is **66 kg**.

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