16 men are able to complete a piece of work in 12 days working 14 hours a day. How long will 28 men, working 12 hours a day, take to complete the work?

Options

A. 10 days
B. 7 days
C. 8 days
D. 6 days

Answer

To solve the problem, we will first determine the total amount of work done in terms of man-hours, and then find out how long it will take for 28 men working 12 hours a day to complete the same amount of work.

### Step 1: Calculate the total work done by 16 men in 12 days working 14 hours a day.

- **Number of men (m1)** = 16
- **Number of days (d1)** = 12
- **Hours worked per day (h1)** = 14

Total work (W) can be calculated as:
\[ W = m1 \times d1 \times h1 \]
Substituting the values:
\[ W = 16 \times 12 \times 14 \]

### Step 2: Perform the multiplication to find the total work.

Calculating:
\[ W = 16 \times 12 = 192 \]
Then,
\[ W = 192 \times 14 = 2688 \text{ man-hours} \]

### Step 3: Determine how many man-hours 28 men working 12 hours a day can provide.

- **Number of men (m2)** = 28
- **Hours worked per day (h2)** = 12

The total work done by 28 men in one day is:
\[ \text{Work done in one day} = m2 \times h2 = 28 \times 12 \]

Calculating:
\[ \text{Work done in one day} = 28 \times 12 = 336 \text{ man-hours} \]

### Step 4: Calculate how many days (d2) it will take for 28 men to complete the total work.

We know the total work is 2688 man-hours and the work done in one day by 28 men is 336 man-hours. We can find the number of days (d2) required by dividing the total work by the work done in one day:
\[ d2 = \frac{W}{\text{Work done in one day}} = \frac{2688}{336} \]

### Step 5: Perform the division to find the number of days.

Calculating:
\[ d2 = \frac{2688}{336} = 8 \]

### Final Answer:
It will take 28 men working 12 hours a day **8 days** to complete the work.

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