X can do `3/4` of a work in 12 days. In how many days X can finish the 1/2 work?

Options

A. 8 days
B. 7 days
C. 6 days
D. None of these

Answer

To solve the problem, we need to determine how many days X can finish half of the work if X can do \( \frac{3}{4} \) of the work in 12 days.

### Step-by-Step Solution:

1. **Understand the Work Done**:
- X can complete \( \frac{3}{4} \) of the work in 12 days.

2. **Calculate the Total Work**:
- Let the total work be represented as \( W \).
- If \( \frac{3}{4} \) of the work is done in 12 days, then the total work \( W \) can be calculated as:
\[ W = \frac{12 \text{ days}}{\frac{3}{4}} = 12 \times \frac{4}{3} = 16 \text{ days} \]
- Therefore, the total work \( W \) is equivalent to 16 days of work.

3. **Determine the Work for Half**:
- Half of the total work is:
\[ \frac{1}{2} W = \frac{1}{2} \times 16 = 8 \text{ days} \]

4. **Calculate the Time Taken for Half the Work**:
- Since X can complete the total work in 16 days, to find out how many days X will take to complete half the work, we can use the relationship:
\[ \text{Time for half work} = \frac{1}{2} \times \text{Total Time} = \frac{1}{2} \times 16 = 8 \text{ days} \]

### Conclusion:
X can finish half of the work in **8 days**.