If a 32 year old man is replaced by a new man,then the average age of 42 men increases by 1 year. What is the age of the new man?

Options

A. 72 years
B. 75 years
C. 74 years
D. 73 years

Answer

To solve the problem, we need to find the age of the new man who replaces a 32-year-old man, resulting in an increase in the average age of 42 men by 1 year.

### Step-by-step Solution:

1. **Understand the initial average age**:
Let the initial average age of the 42 men be \( A \).

2. **Calculate the total initial age**:
The total age of the 42 men can be calculated as:
\[ \text{Total age} = 42 \times A \]

3. **Effect of replacing the 32-year-old man**:
When the 32-year-old man is replaced by a new man whose age we will denote as \( x \), the new total age becomes:
\[ \text{New total age} = (42A - 32 + x) \]

4. **New average age after replacement**:
The new average age of the 42 men is given to be \( A + 1 \). Therefore, we can express the new total age in terms of the new average:
\[ \text{New total age} = 42 \times (A + 1) = 42A + 42 \]

5. **Set up the equation**:
Now we can set the two expressions for the new total age equal to each other:
\[ 42A - 32 + x = 42A + 42 \]

6. **Simplify the equation**:
By simplifying the equation, we can eliminate \( 42A \) from both sides:
\[ -32 + x = 42 \]

7. **Solve for \( x \)**:
Rearranging the equation gives:
\[ x = 42 + 32 = 74 \]

8. **Conclusion**:
Therefore, the age of the new man is \( 74 \) years.

### Final Answer:
The age of the new man is **74 years**.