The average weight of 12 crewmen in a boat is increased by `1/3` kg, when one of the crewmen whose weight is 55kg is replaced by a new man. What is the weight of that new man?

Options

A. 58 kg
B. 60 kg
C. 57 kg
D. 59 kg

Answer

To find the weight of the new man who replaces the crewman weighing 55 kg, we can follow these steps:

### Step 1: Understand the change in average
The average weight of the crewmen increases by \( \frac{1}{3} \) kg when one crewman is replaced. This means that the total weight of the crewmen has increased.

### Step 2: Calculate the total increase in weight
Since there are 12 crewmen, the total increase in weight can be calculated as:
\[ \text{Total Increase} = \text{Number of Crewmen} \times \text{Increase in Average} = 12 \times \frac{1}{3} = 4 \text{ kg} \]

### Step 3: Set up the equation for total weight
Let the original total weight of the 12 crewmen be \( S \). After replacing the 55 kg crewman with the new man (let's denote the weight of the new man as \( x \)), the new total weight becomes:
\[ S - 55 + x \]

### Step 4: Relate the new total weight to the increase
Since we know the total weight has increased by 4 kg, we can set up the equation:
\[ S - 55 + x = S + 4 \]

### Step 5: Simplify the equation
Now, we can simplify the equation:
\[ -55 + x = 4 \]
\[ x = 4 + 55 \]
\[ x = 59 \text{ kg} \]

### Conclusion
The weight of the new man is **59 kg**.

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