There is a 4% increase in volume when a liquid freezes to its solid state. The percentage decrease when solid melts to liquid again, is

Options

A. `3(11)/(13)`
B. `4%`
C. `4(1)/(13)%`
D. `3(1)/(13)%`

Answer

To solve the problem, we need to determine the percentage decrease in volume when a solid melts back into a liquid, given that there is a 4% increase in volume when the liquid freezes.

### Step-by-Step Solution:

1. **Understand the Initial Volume**:
Let's assume the initial volume of the liquid is 100 units.

2. **Calculate the Volume After Freezing**:
When the liquid freezes, its volume increases by 4%.
\[ \text{Volume after freezing} = 100 + (4\% \text{ of } 100) = 100 + 4 = 104 \text{ units} \]

3. **Determine the Volume When Melting**:
When the solid melts back into a liquid, it will return to its original volume. Therefore, the volume of the solid (which is now melting) is 104 units, and it will decrease back to 100 units.

4. **Calculate the Decrease in Volume**:
The decrease in volume when the solid melts is:
\[ \text{Decrease} = 104 - 100 = 4 \text{ units} \]

5. **Calculate the Percentage Decrease**:
To find the percentage decrease, we use the formula:
\[ \text{Percentage Decrease} = \left(\frac{\text{Decrease}}{\text{Original Volume}}\right) \times 100 \]
Here, the original volume (when the solid is in its solid state) is 104 units.
\[ \text{Percentage Decrease} = \left(\frac{4}{104}\right) \times 100 \]

6. **Simplify the Calculation**:
\[ \text{Percentage Decrease} = \left(\frac{4 \times 100}{104}\right) = \frac{400}{104} \approx 3.846\% \]

7. **Final Result**:
Rounding to two decimal places, the percentage decrease when the solid melts back to liquid is approximately **3.85%**.

### Summary of Steps:
- Start with an assumed volume of 100 units.
- Calculate the new volume after a 4% increase.
- Determine the decrease when the solid melts back to liquid.
- Calculate the percentage decrease based on the solid's volume.