The average weight of 12 boxes is 63 kg. If four boxes having an average weight of 70 kg are removed, then what will be new average weight of the remaining boxes?

Options

A. 60 kg
B. 59 kg
C. 60.5 kg
D. 59.5 kg

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total weight of the 12 boxes.
The average weight of the 12 boxes is given as 63 kg. We can find the total weight by multiplying the average weight by the number of boxes.

\[ \text{Total weight of 12 boxes} = \text{Average weight} \times \text{Number of boxes} = 63 \, \text{kg} \times 12 = 756 \, \text{kg} \]

### Step 2: Calculate the total weight of the 4 boxes that are removed.
The average weight of the 4 boxes is given as 70 kg. We can find the total weight of these boxes by multiplying their average weight by the number of boxes.

\[ \text{Total weight of 4 boxes} = \text{Average weight} \times \text{Number of boxes} = 70 \, \text{kg} \times 4 = 280 \, \text{kg} \]

### Step 3: Calculate the total weight of the remaining boxes.
To find the total weight of the remaining boxes after removing the 4 boxes, we subtract the total weight of the 4 boxes from the total weight of the 12 boxes.

\[ \text{Total weight of remaining boxes} = \text{Total weight of 12 boxes} - \text{Total weight of 4 boxes} = 756 \, \text{kg} - 280 \, \text{kg} = 476 \, \text{kg} \]

### Step 4: Calculate the number of remaining boxes.
After removing 4 boxes from the original 12 boxes, the number of remaining boxes is:

\[ \text{Number of remaining boxes} = 12 - 4 = 8 \]

### Step 5: Calculate the new average weight of the remaining boxes.
To find the new average weight, we divide the total weight of the remaining boxes by the number of remaining boxes.

\[ \text{New average weight} = \frac{\text{Total weight of remaining boxes}}{\text{Number of remaining boxes}} = \frac{476 \, \text{kg}}{8} = 59.5 \, \text{kg} \]

### Final Answer:
The new average weight of the remaining boxes is **59.5 kg**.

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