A man can complete a job in 40 days working 6 hours a day. He started ...
Analysis of the Problem:
- Let's start by calculating the work efficiency of each person. The first person can complete the job in 40 days working 6 hours a day, which means he can complete 1/240th of the job in 1 hour.
- The second person can complete the job in half the time, so his work efficiency is double that of the first person, i.e., he can complete 1/120th of the job in 1 hour.
- The third person can complete the job thrice as fast as the first person, so his work efficiency is three times that of the first person, i.e., he can complete 1/80th of the job in 1 hour.
Calculating the Total Work:
- Since the first person works for 6 hours a day, the total work done by him in a day is 6 * 1/240 = 1/40th of the job.
- The second person works for 8 hours a day (as per the problem statement), so the total work done by him in a day is 8 * 1/120 = 1/15th of the job.
- Similarly, the third person works for 8 hours a day, so the total work done by him in a day is 8 * 1/80 = 1/10th of the job.
Calculating the Days to Complete the Work:
- Let's assume the total work is represented by 1 unit.
- On the first day, the first person completes 1/40th of the job.
- On the second day, the first person completes another 1/40th, and the second person completes 1/15th of the job.
- On the third day, the first person completes 1/40th, the second person completes 1/15th, and the third person completes 1/10th of the job.
- This process continues until the entire work is completed.
Conclusion:
- By calculating the work done each day by each person and adding it up until the total work is completed, we can determine the number of days it will take to complete the job.