Entrance Exams
Govt. Exams
60% work is done in 9 days.
Rate = 0.6/9 = 1/15 per day.
Total days = 1/(1/15) = 15 days
A+B rate = 1/6 + 1/8 = 7/24.
Work in 2 days = 14/24 = 7/12.
Remaining = 5/12.
All three rate = 1/6 + 1/8 + 1/12 = 9/24 = 3/8.
Days = (5/12)/(3/8) = 40/36 ≈ 1.11, recalculating: remaining work done in 2 days
Let A's rate = 1/x, B's rate = 1/y.
From equations: 3/x + 2/y = 1/4 and 2/x + 3/y = 1/3.
Solving: x = 30 days
Combined rate = 1/8, A's rate = 1/12. B's rate = 1/8 - 1/12 = 3/24 - 2/24 = 1/24. B takes 24 days
A completes 1/3 work in 5 days, so rate = 1/15 per day.
Remaining work = 2/3.
Days needed = (2/3)/(1/15) = (2/3) × 15 = 10 days
Combined rate = 1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5.
Time = 5 days
This question tests the concept of inverse proportionality between the number of workers and the time required to complete a fixed task.
Work is constant regardless of the number of workers, so we multiply workers by days.
With 10 workers, the same 40 worker-days of work must be completed.
Divide total work by the number of workers to find days required.
When 10 workers work together, they will build the same wall in 4 days.
A's rate = 1/12, B's rate = 1/18.
Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36.
Time = 36/5 = 7.2 days
This question asks us to find B's daily work rate when the total job can be completed in 15 days.
Work rate is the fraction of total work completed per day.
Since B completes the entire job, the total work equals 1.
B completes the job in 15 days, so divide the work by the number of days.
B's work rate is 1/15 of the job per day, which means B completes one-fifteenth of the job each day for 15 days to finish it completely.
This question tests the concept of work rate and how much work is completed in a given time period.
A completes the entire work in 20 days, so the work rate is 1 part per day.
Multiply the daily work rate by the number of days.
Reduce the fraction to its simplest form by dividing both numerator and denominator by 5.
A will complete 1/4 of the work in 5 days.