The average weight of 10 men is increased by 1.5 kg when one of the men who weights 68 kg is replaced by a new man. Find the weight of the new man.

Options

A. 73 Kg
B. 83 Kg
C. 88 Kg
D. 78 Kg

Answer

To find the weight of the new man, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The average weight of 10 men increases by 1.5 kg when a man weighing 68 kg is replaced by a new man.
- Let the initial average weight of the 10 men be \( x \).

2. **Calculate the Total Weight of the 10 Men**:
- The total weight of the 10 men can be expressed as:
\[ \text{Total Weight} = 10 \times x = 10x \]

3. **Determine the New Average Weight**:
- After replacing the 68 kg man, the new average weight becomes:
\[ \text{New Average} = x + 1.5 \]

4. **Calculate the New Total Weight**:
- The new total weight of the 10 men, after the replacement, is:
\[ \text{New Total Weight} = 10 \times (x + 1.5) = 10x + 15 \]

5. **Set Up the Equation**:
- The new total weight can also be expressed as the old total weight minus the weight of the replaced man plus the weight of the new man:
\[ \text{New Total Weight} = 10x - 68 + Y \]
- Here, \( Y \) is the weight of the new man.

6. **Equate the Two Expressions for New Total Weight**:
- We can set the two expressions for the new total weight equal to each other:
\[ 10x + 15 = 10x - 68 + Y \]

7. **Simplify the Equation**:
- Cancel \( 10x \) from both sides:
\[ 15 = -68 + Y \]

8. **Solve for \( Y \)**:
- Rearranging gives:
\[ Y = 15 + 68 = 83 \]

9. **Conclusion**:
- The weight of the new man is \( 83 \) kg.

### Final Answer:
The weight of the new man is **83 kg**.