75 men can complete a work in 30 days 20 days later they are joined by 50 more men but the efficiency of these new men is 50% of the efficiency of the existing men in how many days less than the schedule time will the work completed?
Answers
Answer:
Work will be completed in 2.5 days less than the scheduled time
Step-by-step explanation:
Given that 75 men can complete work in 30 days
Total work = 75 × 30 man days work
In 30 days, work done = 75 × 30 man days work = 2250 man days work
In 1 day, work done = 75 man days work
In 20 days, work done = 75 × 20 man days work = 1500 man days work
Work left after 20 days = (2250 - 1500) man days work = 750 man days work
Given that 50 more men joined after day 20 with 50% efficiency
That means 100% efficiency or 1 man day work is done by 2 men
Thus, effective men with 100% efficiency joining after day 20 is 25
Total men with 100% efficiency = 75 + 25 = 100 men
100 man days work done in 1 day
750 man days work done in = (1/100) × 750 = 750/100 = 7.5 days
Total time take with more men = 20 + 7.5 = 27.5 days
Thus, work will be completed in 2.5 days less than the scheduled time