If l0 men and 20 women can complete a given task in 24 hours and efficiency of one woman is half of that of one , man, in how many hours can 60 women complete the same work ?

Options

A. 20
B. 30
C. 16
D. 27

Answer

To solve the problem, we need to determine how many hours 60 women will take to complete the same task that 10 men and 20 women can complete in 24 hours. We also know that the efficiency of one woman is half that of one man.

### Step-by-Step Solution:

1. **Determine the total work done in man-hours:**
- Let the efficiency of one man be \( M \) (man-hours).
- Therefore, the efficiency of one woman is \( \frac{M}{2} \).
- The total work done by 10 men and 20 women in 24 hours can be calculated as:
\[ \text{Total Work} = (\text{Number of Men} \times \text{Efficiency of Man} + \text{Number of Women} \times \text{Efficiency of Woman}) \times \text{Time} \]
\[ = (10 \times M + 20 \times \frac{M}{2}) \times 24 \]
\[ = (10M + 10M) \times 24 = 20M \times 24 = 480M \]

2. **Calculate the work done by 60 women:**
- The efficiency of 60 women is:
\[ \text{Efficiency of 60 Women} = 60 \times \frac{M}{2} = 30M \]
- Let \( T \) be the time taken by 60 women to complete the same work. The total work done by 60 women can also be expressed as:
\[ \text{Total Work} = \text{Efficiency of 60 Women} \times T = 30M \times T \]

3. **Set the total work equations equal to each other:**
- Since both expressions represent the same total work, we can set them equal:
\[ 30M \times T = 480M \]

4. **Solve for \( T \):**
- Dividing both sides by \( 30M \):
\[ T = \frac{480M}{30M} = 16 \text{ hours} \]

### Final Answer:
Thus, 60 women can complete the same work in **16 hours**.