The average weight of 25 boxes in a boat is increased by 2 kg when one of the boxes weighing 68 kg is replaced by a new box. The weight (in kg) of the new box is:

Options

A. 70
B. 118
C. 132
D. 97

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
We know that the average weight of 25 boxes increases by 2 kg when a box weighing 68 kg is replaced by a new box. We need to find the weight of the new box.

### Step 2: Define the average weight
Let the original average weight of the 25 boxes be \( y \) kg.

### Step 3: Calculate the total weight of the original boxes
The total weight of the 25 boxes can be calculated using the formula for average:
\[ \text{Total weight} = \text{Average weight} \times \text{Number of boxes} \]
Thus, the total weight of the 25 boxes is:
\[ \text{Total weight} = y \times 25 \]

### Step 4: Determine the new average weight
When one box weighing 68 kg is replaced, the average weight increases by 2 kg. Therefore, the new average weight becomes:
\[ \text{New average weight} = y + 2 \]

### Step 5: Calculate the total weight after replacement
After replacing the box, the total weight of the boxes becomes:
\[ \text{New total weight} = (y + 2) \times 25 \]

### Step 6: Set up the equation
The new total weight can also be expressed as the old total weight minus the weight of the box being replaced plus the weight of the new box. Therefore, we can write:
\[ \text{New total weight} = \text{Old total weight} - 68 + \text{Weight of new box} \]
Substituting the expressions we have:
\[ (y + 2) \times 25 = y \times 25 - 68 + \text{Weight of new box} \]

### Step 7: Simplify the equation
Expanding both sides:
\[ 25y + 50 = 25y - 68 + \text{Weight of new box} \]
Now, we can cancel \( 25y \) from both sides:
\[ 50 = -68 + \text{Weight of new box} \]

### Step 8: Solve for the weight of the new box
Adding 68 to both sides gives:
\[ 50 + 68 = \text{Weight of new box} \]
\[ \text{Weight of new box} = 118 \text{ kg} \]

### Final Answer
The weight of the new box is **118 kg**.

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