The average weight of 10 women is increased by 1 kg if 2 women of 42 kg and 38 kg are replaced by 2 men. Find the average weight of both the men.

Options

A. 46kg
B. 45kg
C. 42kg
D. 44kg

Answer

To solve the problem, let's break it down step by step.

### Step 1: Understand the average weight of the women
Let the average weight of the 10 women be \( x \) kg. Therefore, the total weight of the 10 women can be expressed as:
\[ \text{Total weight of women} = 10x \]

### Step 2: Calculate the new average weight
According to the problem, the average weight of the women increases by 1 kg when 2 women are replaced by 2 men. Thus, the new average weight becomes:
\[ \text{New average weight} = x + 1 \text{ kg} \]
The total weight of the women after the replacement is:
\[ \text{Total weight after replacement} = 10(x + 1) = 10x + 10 \]

### Step 3: Calculate the total weight of the replaced women
The two women being replaced weigh 42 kg and 38 kg. Therefore, the total weight of these two women is:
\[ \text{Total weight of replaced women} = 42 + 38 = 80 \text{ kg} \]

### Step 4: Set up the equation for the total weight after replacement
Let the total weight of the two men be \( y \) kg. After replacing the two women with the two men, the total weight can also be expressed as:
\[ \text{Total weight after replacement} = (10x - 80) + y \]

### Step 5: Equate the two expressions for total weight after replacement
Now, we can set the two expressions for the total weight after replacement equal to each other:
\[ 10x + 10 = (10x - 80) + y \]

### Step 6: Simplify the equation
Now, simplify the equation:
\[ 10x + 10 = 10x - 80 + y \]
Subtract \( 10x \) from both sides:
\[ 10 = -80 + y \]
Now, add 80 to both sides:
\[ y = 10 + 80 = 90 \text{ kg} \]

### Step 7: Find the average weight of the two men
Since \( y \) is the total weight of the two men, the average weight of the two men can be calculated as:
\[ \text{Average weight of the men} = \frac{y}{2} = \frac{90}{2} = 45 \text{ kg} \]

### Final Answer
The average weight of both the men is **45 kg**.

---