If 20 men working 7 hours a day can do a piece of work in 10 days, in how many days will 15 men working 8 hours a day do the same piece of work?

Options

A. `15""5/(21)` days
B. `11""2/3` days
C. `6""9/(16)` days
D. `4""1/5` days

Answer

To solve the problem, we will use the concept of man-hours, which is the total amount of work done by a certain number of men in a certain number of hours.

### Step 1: Calculate the total work done in man-hours by the first group of workers.

Given:
- Number of men = 20
- Hours worked per day = 7
- Days taken = 10

Total work (in man-hours) = Number of men × Hours per day × Days
\[ \text{Total work} = 20 \text{ men} \times 7 \text{ hours/day} \times 10 \text{ days} = 1400 \text{ man-hours} \]

### Step 2: Determine how many man-hours are needed for the second group of workers to complete the same work.

We already calculated that the total work required is 1400 man-hours.

### Step 3: Calculate the number of days required for the second group of workers.

Given:
- Number of men = 15
- Hours worked per day = 8

Now, we need to find out how many days (let's denote it as \(d\)) it will take for 15 men working 8 hours a day to complete 1400 man-hours of work.

The total work done by 15 men in \(d\) days is:
\[ \text{Total work} = 15 \text{ men} \times 8 \text{ hours/day} \times d \text{ days} \]

Setting this equal to the total work required:
\[ 15 \times 8 \times d = 1400 \]

### Step 4: Solve for \(d\).

\[ 120d = 1400 \]
\[ d = \frac{1400}{120} = \frac{35}{3} \approx 11.67 \text{ days} \]

Thus, it will take approximately 11.67 days for 15 men working 8 hours a day to complete the same piece of work.

### Final Answer:
15 men working 8 hours a day will complete the work in approximately 11.67 days.

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