A box weighs 8.5 kg when full of sand and weighs 5.5 kg when it is half filled with sand. The weight of the empty box is :

Options

A. 5 kg
B. 6 kg
C. 2.5 kg
D. 4.5 kg.

Answer

To find the weight of the empty box, we can set up equations based on the information given in the problem.

### Step 1: Define Variables
Let:
- \( X \) = weight of the empty box (in kg)
- \( Y \) = weight of the sand when the box is full (in kg)

### Step 2: Set Up Equations
From the problem, we have two scenarios:
1. When the box is full of sand, the total weight is 8.5 kg:
\[ X + Y = 8.5 \quad \text{(Equation 1)} \]

2. When the box is half filled with sand, the total weight is 5.5 kg:
\[ X + \frac{Y}{2} = 5.5 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 2 for Y
To eliminate \( Y \), we can manipulate Equation 2:
\[ X + \frac{Y}{2} = 5.5 \]
Multiply the entire equation by 2 to eliminate the fraction:
\[ 2X + Y = 11 \quad \text{(Equation 3)} \]

### Step 4: Set Up a System of Equations
Now we have two equations:
1. \( X + Y = 8.5 \) (Equation 1)
2. \( 2X + Y = 11 \) (Equation 3)

### Step 5: Eliminate Y
Subtract Equation 1 from Equation 3:
\[ (2X + Y) - (X + Y) = 11 - 8.5 \]
This simplifies to:
\[ 2X - X = 2.5 \]
\[ X = 2.5 \]

### Step 6: Conclusion
The weight of the empty box \( X \) is 2.5 kg.