| (1) | 20 days | (2) | 40 days | (3) | 30 days | (4) | 24 days |
Solution:
Let a be the number of days in which A can do the job alone. Therefore, working alone, A will complete 1/a th of the job in a day.
Similarly, let b the number of days in which B can do the job alone. Hence, B will complete 1/b th of the job in a day.
Working together, A and B will complete (1/a + 1/b) th of the job in a day. The problem states that working together, A and B will complete the job in 7.5 or 15/2 days. i.e they will complete 2/15th of the job in a day.
Therefore,1/a + 1/b = 2/15 -(1)
From statement 2 of the question, we know that if A completes half the job working alone and B takes over and completes the next half, they will take 20 days.
As A can complete the job working alone in �a� days, he will complete half the job, working alone, in a/2 days.
Similarly, B will complete the remaining half of the job in b/2 days.
Therefore,a/2+b/2 = 20 => a+b = 40 or a = 40 - b - (2)
From (1) and (2) we get, 1 / 40-b + 1/b = 2/15 => 600=2b(40-b)
=> 600 = 80b - 2b2
=> b2 - 40b + 300 = 0
=> (b - 30)(b - 10) = 0
=> b = 30 or b = 10.
If b = 30, then a = 40 - 30 = 10 or
If b = 10, then a = 40 - 10 = 30.
As A is more efficient then B, he will take lesser time to do the job alone. Hence A will take only 10 days and B will take 30 days.
Note: Whenever you encounter work time problems, always find out how much of the work will be completed by A in unit time (an hour, a day, a month etc). Find out how much of the work will be completed by B in unit time and add those to find the amount of work that will be completed in unit time.
If �A� takes 10 days to do a job, he will do 1/10th of the job in a day. Similarly, if 2/5ths of the job is done in a day, the entire job will be done in 5/2 days.
