8 men working for 9 hours a day can complete a piece of work in 20 days. In how many days can 7 men working for 10 hours a day complete the same piece of work?

Options

A. `20""1/2` days
B. `20""3/5` days
C. `21 days `
D. `20""4/7` days

Answer

To solve the problem, we need to determine how many days it will take for 7 men working 10 hours a day to complete the same piece of work that 8 men can complete in 20 days working 9 hours a day.

### Step-by-Step Solution:

1. **Calculate the Total Work Done**:
- The total work done can be calculated in terms of man-hours.
- If 8 men work for 9 hours a day for 20 days, the total work (in man-hours) is:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Number of Days} \]
\[ \text{Total Work} = 8 \text{ men} \times 9 \text{ hours/day} \times 20 \text{ days} = 1440 \text{ man-hours} \]

2. **Calculate the Daily Work Done by 7 Men**:
- Now, we need to calculate how much work 7 men can do in one day working 10 hours.
- The work done by 7 men in one day is:
\[ \text{Daily Work} = 7 \text{ men} \times 10 \text{ hours/day} = 70 \text{ man-hours/day} \]

3. **Calculate the Number of Days Required**:
- To find the number of days required for 7 men to complete the total work of 1440 man-hours, we divide the total work by the daily work:
\[ \text{Number of Days} = \frac{\text{Total Work}}{\text{Daily Work}} = \frac{1440 \text{ man-hours}}{70 \text{ man-hours/day}} = 20.57 \text{ days} \]
- Since we typically round up to the nearest whole number when dealing with days, we can say it will take approximately 21 days.

### Final Answer:
7 men working for 10 hours a day can complete the same piece of work in approximately **21 days**.