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Work Time Practice Question - CAT 2012 Prep

Question 1

If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?

(1) 20 days
(2) 40 days
(3) 36 days
(4) 24 days
(5) 30 days

Correct Choice - (5). Correct Answer is 30 days

Explanatory Answer

Let 'a' be the number of days in which A can do the job alone. Therefore, working alone, A will complete of the job in a day.

Similarly, let 'b' be the number of days in which B can do the job alone. Hence, B will complete of the job in a day.

Working together, A and B will complete 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)

From 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 days.
Similarly, B will complete the remaining half of the job in days.
Therefore, => a + b = 40 or a = 40 - b ...... (2)

From (1) and (2) we get, => 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 than 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 can 'A' complete in a unit time (an hour, a day, a month etc). Find out how much of the work can be completed by 'B' in a unit time. Then add the amount of work done by A and B to find the total amount of work that will be completed in a 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.

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