The average weight of 5 men is decreased by 3 kg when one of them weighing 150 kg is replaced by another person. This new person is again replaced by another person whose weight is 30 kg lower than the person he replaced. What is the overall change in the average due to this dual change?

Options

A. 6 kg
B. 9 kg
C. 12 kg
D. 15 kg

Answer

To solve the problem step by step, we will analyze the changes in the average weight of the 5 men due to the replacements.

### Step 1: Calculate the initial total weight of the 5 men.
Let the average weight of the 5 men be \( A \). Therefore, the total weight of the 5 men can be expressed as:
\[ \text{Total Weight} = 5A \]

### Step 2: Determine the effect of replacing the first man.
When the man weighing 150 kg is replaced, the average decreases by 3 kg. Thus, the new average weight becomes:
\[ A - 3 \]
The new total weight after replacing the 150 kg man can be expressed as:
\[ \text{New Total Weight} = 5(A - 3) = 5A - 15 \]
This means that the weight of the new man (let's call him \( x \)) can be calculated as follows:
\[ 5A - 15 = (5A - 150) + x \]
Rearranging gives us:
\[ x = 150 - 15 = 135 \text{ kg} \]

### Step 3: Determine the effect of replacing the second man.
Now, the new man weighing 135 kg is replaced by another person whose weight is 30 kg lower. Thus, the weight of the new person (let's call him \( y \)) is:
\[ y = 135 - 30 = 105 \text{ kg} \]

### Step 4: Calculate the total weight after both replacements.
After the second replacement, the total weight of the 5 men becomes:
\[ \text{Final Total Weight} = (5A - 15) - 135 + 105 = 5A - 15 - 30 = 5A - 45 \]

### Step 5: Calculate the new average weight.
The new average weight after both replacements can be calculated as:
\[ \text{New Average} = \frac{5A - 45}{5} = A - 9 \]

### Step 6: Determine the overall change in average.
The overall change in average weight is:
\[ \text{Change in Average} = \text{New Average} - \text{Original Average} = (A - 9) - A = -9 \text{ kg} \]

Thus, the overall change in the average weight due to the dual change is a decrease of 9 kg.

### Final Answer:
The overall change in the average weight is **9 kg decrease**.

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