The average weight of 15 men is increased by 1.6 kg when one of the man, who weights 42 kg is replaced by a new man. Find the weight of the new man (in kg).

Options

A. 65
B. 66
C. 43
D. 67

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Understand the problem
We know that the average weight of 15 men is increased by 1.6 kg when one man weighing 42 kg is replaced by a new man. We need to find the weight of the new man.

### Step 2: Define variables
Let the initial average weight of the 15 men be \( x \) kg. Therefore, the total weight of the 15 men can be expressed as:
\[ \text{Total weight} = 15x \text{ kg} \]

### Step 3: Calculate the new average weight
When the man weighing 42 kg is replaced, the new average weight becomes \( x + 1.6 \) kg. Thus, the new total weight of the 15 men will be:
\[ \text{New total weight} = 15(x + 1.6) \text{ kg} \]

### Step 4: Set up the equation
The new total weight can also be expressed as the old total weight minus the weight of the man being replaced plus the weight of the new man. Therefore, we can write:
\[ 15x - 42 + y = 15(x + 1.6) \]
where \( y \) is the weight of the new man.

### Step 5: Simplify the equation
Now, let's simplify the equation:
\[ 15x - 42 + y = 15x + 24 \]
Here, \( 15 \times 1.6 = 24 \).

### Step 6: Solve for \( y \)
Now, we can isolate \( y \):
\[ y = 15x + 24 + 42 - 15x \]
This simplifies to:
\[ y = 24 + 42 \]
\[ y = 66 \text{ kg} \]

### Conclusion
The weight of the new man is \( 66 \) kg.

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