10 men working 8 hours day can do a work in 30 days. In how many days will 12 men working 4 hours a day take do the same work?

Options

A. A)40 days
B. B)60 days
C. C)50 days
D. D)30 days

Answer

To solve the problem, we need to determine how many days it will take for 12 men working 4 hours a day to complete the same work that 10 men can complete in 30 days working 8 hours a day.

### Step-by-step Solution:

1. **Calculate the total work done in man-hours by the first group:**
- Number of men = 10
- Hours per day = 8
- Number of days = 30

Total work (in man-hours) = Number of men × Hours per day × Number of days
\[ \text{Total work} = 10 \, \text{men} \times 8 \, \text{hours/day} \times 30 \, \text{days} = 2400 \, \text{man-hours} \]

2. **Set up the equation for the second group:**
- Number of men = 12
- Hours per day = 4
- Number of days = \(d_2\) (unknown)

Total work done by the second group can be expressed as:
\[ \text{Total work} = 12 \, \text{men} \times 4 \, \text{hours/day} \times d_2 \, \text{days} \]

3. **Equate the total work from both groups:**
Since both groups are doing the same work, we can set the equations equal to each other:
\[ 2400 \, \text{man-hours} = 12 \, \text{men} \times 4 \, \text{hours/day} \times d_2 \]

4. **Simplify the equation:**
\[ 2400 = 48 \, d_2 \]

5. **Solve for \(d_2\):**
\[ d_2 = \frac{2400}{48} = 50 \]

Thus, it will take 12 men working 4 hours a day a total of **50 days** to complete the same work.