A group of men decided to complete a job in 4 days. However, since 10 men dropped out every day, the job got completed at the end of the 7th day. How many men were there in the beginning?
- A140
- B70
- C35
- D90
Solution & Step-by-step Explanation
Let the initial number of men be x.
Let the efficiency of one man be 1 unit of work per day.
Total work to be done = 4×x=4x units.
According to the given condition, 10 men drop out every day, and the work finishes in 7 days.
The number of men working on consecutive days is:
Day 1: x
Day 2: x−10
Day 3: x−20
Day 4: x−30
Day 5: x−40
Day 6: x−50
Day 7: x−60
Total work done in these 7 days:
Total Work=x+(x−10)+(x−20)+(x−30)+(x−40)+(x−50)+(x−60)
4x=7x−(10+20+30+40+50+60)
4x=7x−210
3x=210
x=70
Thus, there were 70 men in the beginning.
Let the efficiency of one man be 1 unit of work per day.
Total work to be done = 4×x=4x units.
According to the given condition, 10 men drop out every day, and the work finishes in 7 days.
The number of men working on consecutive days is:
Day 1: x
Day 2: x−10
Day 3: x−20
Day 4: x−30
Day 5: x−40
Day 6: x−50
Day 7: x−60
Total work done in these 7 days:
Total Work=x+(x−10)+(x−20)+(x−30)+(x−40)+(x−50)+(x−60)
4x=7x−(10+20+30+40+50+60)
4x=7x−210
3x=210
x=70
Thus, there were 70 men in the beginning.