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, we need to find the weight of the new man (let's denote it as N kg) who replaces one of the oarsmen weighing 42 kg, resulting in an increase in the average weight of the crew.

### Step-by-Step Solution:

1. **Understand the Average Weight Change**:
- The average weight of the 15 oarsmen increases by 1.6 kg after replacing the 42 kg oarsman.

2. **Calculate the Total Weight Before Replacement**:
- Let the average weight of the oarsmen before the replacement be \( x \) kg.
- The total weight of the 15 oarsmen before replacement is \( 15x \) kg.

3. **Calculate the Total Weight After Replacement**:
- After replacing the 42 kg oarsman with the new man weighing \( N \) kg, the total weight becomes:
\[ \text{Total Weight After} = 15x - 42 + N \]

4. **Determine the New Average Weight**:
- The new average weight after the replacement is \( x + 1.6 \) kg.
- Therefore, the total weight after replacement can also be expressed as:
\[ \text{Total Weight After} = 15(x + 1.6) = 15x + 24 \]

5. **Set Up the Equation**:
- Now we can set the two expressions for total weight after replacement equal to each other:
\[ 15x - 42 + N = 15x + 24 \]

6. **Solve for N**:
- Simplifying the equation:
\[ N - 42 = 24 \]
\[ N = 24 + 42 \]
\[ N = 66 \]

Thus, the weight of the new man is **66 kg**.