When water is changed into ice, its volume increases by `9%` . If ice changes into water, the `%` decrease in volume is ?

Options

A. `88(28)/(109)%`
B. `6(28)/(109)%`
C. `8(21)/(109)%`
D. `7(27)/(109)%`

Answer

To solve the problem, we need to find the percentage decrease in volume when ice melts back into water, given that the volume of water increases by 9% when it turns into ice.

### Step-by-Step Solution:

1. **Assume the Initial Volume of Water**:
Let's assume the volume of water is 100 units.

**Hint**: Start with a simple value to make calculations easier.

2. **Calculate the Volume of Ice**:
When water changes into ice, its volume increases by 9%.
Therefore, the new volume of ice can be calculated as:
\[ \text{Volume of ice} = \text{Initial volume} + \text{Increase in volume} \]
\[ \text{Volume of ice} = 100 + (9\% \text{ of } 100) = 100 + 9 = 109 \text{ units} \]

**Hint**: Remember to calculate the increase based on the initial volume.

3. **Calculate the Volume of Water After Melting**:
When ice melts back into water, it returns to its original volume of 100 units.

**Hint**: The volume of water after melting is the same as the initial volume of water.

4. **Calculate the Decrease in Volume**:
The decrease in volume when ice turns back into water is:
\[ \text{Decrease in volume} = \text{Volume of ice} - \text{Volume of water} \]
\[ \text{Decrease in volume} = 109 - 100 = 9 \text{ units} \]

**Hint**: Subtract the final volume from the initial volume of ice to find the decrease.

5. **Calculate the Percentage Decrease in Volume**:
The percentage decrease in volume can be calculated using the formula:
\[ \text{Percentage decrease} = \left( \frac{\text{Decrease in volume}}{\text{Volume of ice}} \right) \times 100 \]
\[ \text{Percentage decrease} = \left( \frac{9}{109} \right) \times 100 \approx 8.26\% \]

**Hint**: Use the volume of ice as the base for calculating the percentage decrease.

### Final Answer:
The percentage decrease in volume when ice changes back into water is approximately **8.26%**.