30 men working 5 hours a day can do a task in 16 days in how many days will 40 men working 6 hours a day fo the same task ?
A. 12 days
B. 10 days
C. 15 days
D. 18 days

Options

A. C
B. B
C. A
D. D

Answer

To solve the problem, let's break it down step by step.

### Step 1: Understand the given information
We know that:
- 30 men work 5 hours a day for 16 days to complete a task.
- We need to find out how many days (d2) it will take for 40 men working 6 hours a day to complete the same task.

### Step 2: Calculate the total work done in man-hours
The total work (W) done by the first group of men can be calculated using the formula:
\[ W = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]

For the first group:
\[ W = 30 \text{ men} \times 5 \text{ hours/day} \times 16 \text{ days} \]
\[ W = 30 \times 5 \times 16 \]
\[ W = 2400 \text{ man-hours} \]

### Step 3: Set up the equation for the second group
Now, we need to find out how many days (d2) it will take for 40 men working 6 hours a day to complete the same amount of work (2400 man-hours).

Using the same formula for the second group:
\[ W = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]
For the second group:
\[ 2400 = 40 \text{ men} \times 6 \text{ hours/day} \times d2 \]

### Step 4: Solve for d2
Now we can rearrange the equation to solve for d2:
\[ 2400 = 40 \times 6 \times d2 \]
\[ 2400 = 240 \times d2 \]
\[ d2 = \frac{2400}{240} \]
\[ d2 = 10 \text{ days} \]

### Conclusion
Thus, it will take 40 men working 6 hours a day a total of **10 days** to complete the same task.

### Answer
**B. 10 days**