The average weight of 8 men is increased by 1.5 kg when one of the men whose weight 65 kg is replaced by a new man. The weight of the new man is:

Options

A. 88 kg
B. 77 kg
C. 63 kg
D. 54 kg

Answer

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

### Step 1: Understand the initial average weight
Let the initial average weight of the 8 men be \( A \). Therefore, the total weight of the 8 men can be expressed as:
\[ \text{Total weight} = 8A \]

### Step 2: Calculate the new average weight
According to the problem, the average weight increases by 1.5 kg when the man weighing 65 kg is replaced. Thus, the new average weight becomes:
\[ \text{New average} = A + 1.5 \]

### Step 3: Calculate the new total weight
With the new average, the total weight of the 8 men after the replacement can be expressed as:
\[ \text{New total weight} = 8(A + 1.5) = 8A + 12 \]

### Step 4: Set up the equation
When the man weighing 65 kg is replaced, the new total weight can also be expressed as:
\[ \text{New total weight} = \text{Old total weight} - 65 + \text{Weight of new man} \]
Substituting the expressions we have:
\[ 8A + 12 = 8A - 65 + \text{Weight of new man} \]

### Step 5: Simplify the equation
Now, we can simplify the equation:
\[ 8A + 12 = 8A - 65 + \text{Weight of new man} \]
Subtract \( 8A \) from both sides:
\[ 12 = -65 + \text{Weight of new man} \]

### Step 6: Solve for the weight of the new man
Now, add 65 to both sides:
\[ \text{Weight of new man} = 12 + 65 = 77 \text{ kg} \]

### Final Answer
The weight of the new man is **77 kg**.

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