A soda water bottle is exactly filled with coke weighs 1600 gm but when it is `1/3` rd filled it weights only 900 gm. The weight of the empty bottle is :

Options

A. 650
B. 1100
C. 550
D. data insufficient.

Answer

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

### Step-by-Step Solution:

1. **Define Variables**:
- Let \( B \) be the weight of the empty bottle.
- Let \( C \) be the weight of the coke when the bottle is full.

2. **Set Up the First Equation**:
- When the bottle is fully filled with coke, the total weight is 1600 grams.
- Therefore, we can write the equation:
\[ B + C = 1600 \quad \text{(1)} \]

3. **Set Up the Second Equation**:
- When the bottle is one-third filled with coke, the total weight is 900 grams.
- Since one-third of the coke is in the bottle, the weight of the coke in this case is \( \frac{1}{3}C \).
- Thus, we can write the second equation:
\[ B + \frac{1}{3}C = 900 \quad \text{(2)} \]

4. **Eliminate \( C \)**:
- To eliminate \( C \), we can multiply the second equation by 3 to make the coefficients of \( C \) the same:
\[ 3B + C = 2700 \quad \text{(3)} \]

5. **Subtract Equation (1) from Equation (3)**:
- Now, we subtract equation (1) from equation (3):
\[ (3B + C) - (B + C) = 2700 - 1600 \]
- This simplifies to:
\[ 3B - B = 2700 - 1600 \]
\[ 2B = 1100 \]

6. **Solve for \( B \)**:
- Divide both sides by 2:
\[ B = \frac{1100}{2} = 550 \]

7. **Conclusion**:
- The weight of the empty bottle \( B \) is 550 grams.

### Final Answer:
The weight of the empty bottle is **550 grams**.