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

Options

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

Answer

To solve the problem step by step, we will use the information given about the average weight of the oarsmen and the changes that occur when one oarsman is replaced.

### Step 1: Understand the given information
We know:
- The average weight of 15 oarsmen increases by 1.6 kg.
- One oarsman weighing 42 kg is replaced by a new oarsman.

### Step 2: Calculate the total weight of the oarsmen before the replacement
Let the average weight of the 15 oarsmen before the replacement be \( x \) kg.
The total weight of the 15 oarsmen can be calculated as:
\[ \text{Total weight before} = 15x \]

### Step 3: Calculate the total weight after the replacement
After replacing the 42 kg oarsman with the new oarsman, the average weight becomes \( x + 1.6 \) kg.
The total weight of the 15 oarsmen after the replacement is:
\[ \text{Total weight after} = 15(x + 1.6) = 15x + 24 \]

### Step 4: Set up the equation based on the total weights
Since the total weight before the replacement and after the replacement must be equal, we can set up the following equation:
\[ 15x - 42 + \text{Weight of new man} = 15x + 24 \]

### Step 5: Simplify the equation
We can simplify the equation:
\[ 15x - 42 + \text{Weight of new man} = 15x + 24 \]
Subtract \( 15x \) from both sides:
\[ -42 + \text{Weight of new man} = 24 \]

### Step 6: Solve for the weight of the new man
Now, we can isolate the weight of the new man:
\[ \text{Weight of new man} = 24 + 42 = 66 \text{ kg} \]

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

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