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

Options

A. 70 kg
B. 74 kg
C. 76 kg
D. 77 kg

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the Problem
We know that the average weight of 8 men increases by 1.5 kg when one man weighing 65 kg is replaced by a new man. We need to find the weight of the new man.

### Step 2: Calculate the Initial Average Weight
Let the initial average weight of the 8 men be \( X \) kg. Therefore, the total weight of the 8 men can be expressed as:
\[ \text{Total weight} = 8X \]

### Step 3: Calculate the New Average Weight
When the man weighing 65 kg is replaced, the new average weight becomes \( X + 1.5 \) kg. Thus, the total weight of the 8 men after the replacement is:
\[ \text{New total weight} = 8(X + 1.5) = 8X + 12 \]

### Step 4: Set Up the Equation
The new total weight can also be expressed as the original total weight minus the weight of the man being replaced plus the weight of the new man:
\[ \text{New total weight} = (8X - 65) + \text{Weight of new man} \]
Let the weight of the new man be \( Y \). Therefore, we can write:
\[ 8X + 12 = (8X - 65) + Y \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ 8X + 12 = 8X - 65 + Y \]
Subtract \( 8X \) from both sides:
\[ 12 = -65 + Y \]
Now, add 65 to both sides:
\[ Y = 12 + 65 \]

### Step 6: Calculate the Weight of the New Man
Now calculate \( Y \):
\[ Y = 77 \text{ kg} \]

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

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