If water is freezed to volume ice, its volume is increased by 10%, then its if the ice is melted to water again, its volume will be decreased by :

Options

A. `9%`
B. `9(1)/(11)%`
C. `8%`
D. `9(1)/(2)%`

Answer

To solve the problem step by step, we will analyze the situation of water being frozen into ice and then melted back into water, focusing on the changes in volume.

### Step-by-Step Solution:

1. **Understanding the Initial Volume of Water**:
- Let's assume the initial volume of water is 100 units (this is a convenient choice for calculation).

**Hint**: Start with a simple volume for easy calculations.

2. **Calculating the Volume of Ice**:
- When water freezes, its volume increases by 10%.
- Therefore, the volume of ice after freezing = Initial volume of water + 10% of Initial volume of water.
- Volume of ice = 100 + (10/100) * 100 = 100 + 10 = 110 units.

**Hint**: Remember that a 10% increase means you add 10% of the original volume to the original volume.

3. **Melting the Ice Back to Water**:
- Now, when the ice melts back into water, we need to determine the volume of water produced.
- The volume of water after melting will be the same as the volume of ice before melting, which is 110 units.

**Hint**: The volume of water after melting will not revert to the original volume; it will be equal to the volume of ice.

4. **Calculating the Decrease in Volume**:
- The initial volume of water was 100 units, and after melting, we have 110 units of water.
- To find the decrease in volume, we compare the initial volume of water with the volume of ice.
- The decrease in volume = Initial volume of water - Volume of water after melting = 100 - 110 = -10 units.

**Hint**: A negative result indicates an increase in volume rather than a decrease.

5. **Calculating the Percentage Decrease**:
- To find the percentage decrease, we can use the formula:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Volume}}{\text{Original Volume}} \right) \times 100 \]
- Here, the change in volume is -10 units (indicating an increase), and the original volume is 100 units.
- Percentage change = \(\left( \frac{-10}{100} \right) \times 100 = -10\%\).

**Hint**: The percentage change can be negative if the volume has increased, indicating a decrease in the original context.

### Final Answer:
The volume of water decreases by 10% when ice is melted back to water.