A man is twice as fast as a woman. Together the man and the woman do the piece of work in 8 days. In how many days each will do the work if engaged alone?
(a)man-14 days, woman-28 days
(b)man-12 days, woman-24 days
(c)man-10 days, woman-20 days
(d)None of these

Options

A. man-14 days, woman-28 days
B. man-12 days, woman-24 days
C. man-10 days, woman-20 days
D. None of these

Answer

To solve the problem, we need to determine how long it will take for a man and a woman to complete a piece of work individually, given that the man is twice as fast as the woman and they can complete the work together in 8 days.

### Step-by-Step Solution:

1. **Define the Rates of Work**:
Let the rate of work done by the woman be \( W \). Since the man is twice as fast, his rate of work will be \( 2W \).

2. **Combined Rate of Work**:
When the man and woman work together, their combined rate of work is:
\[ W + 2W = 3W \]

3. **Total Work Done**:
They complete the work together in 8 days. Therefore, the total work can be expressed as:
\[ \text{Total Work} = \text{Combined Rate} \times \text{Time} = 3W \times 8 = 24W \]

4. **Finding Individual Work Times**:
- For the **man**:
The man does \( 2W \) of work in one day. To find out how many days he will take to complete the total work (24W), we use the formula:
\[ \text{Days for Man} = \frac{\text{Total Work}}{\text{Man's Rate}} = \frac{24W}{2W} = 12 \text{ days} \]

- For the **woman**:
The woman does \( W \) of work in one day. To find out how many days she will take to complete the total work (24W), we use the formula:
\[ \text{Days for Woman} = \frac{\text{Total Work}}{\text{Woman's Rate}} = \frac{24W}{W} = 24 \text{ days} \]

5. **Final Answer**:
Therefore, the man will complete the work in 12 days and the woman will complete the work in 24 days.

### Conclusion:
The answer is:
- Man: 12 days
- Woman: 24 days

Thus, the correct option is (b) man-12 days, woman-24 days.