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Work & Time - Quant/Math - CAT 2010
Question 4 the day:
April 25, 2002
- Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?
| (1) | 8 days |
| (2) | 5 days |
| (3) | 3 days |
| (4) | 7 days |
- How long will it take for A alone to complete the job?
| (1) | 8 days |
| (2) | 6 days |
| (3) | 10 days |
| (4) | 20 days |
Correct Answers
Solution:
Even before you start working on the problem, check out if you can eliminate some answer choices as impossible.
In question (1), we know that if A and B alone work, they can complete the job in 6 days. Therefore, if all three of them A, B and C work together the number of days it will take to complete the job will surely be less than 6 days. Hence, we can eliminate answer choices (1) and (4) right away.
Similarly in question (2), we know that A and B together take 6 days to complete the job. Therefore, A alone will take more than 6 days to complete the job. Therefore, we can eliminate answer choice (2).
In any question, as a rule spend about 5 seconds to see if the answer choices provide any clue to solve the question or help in eliminating one or more obviously absurd choices. This will help you (1) in reducing the time it will take to do the problem and (2) in increasing your probability of success should you choose to take a guess without actually solving the problem.
Question 1 Let A be the number of days that A will take to complete the job alone, B days for B to complete the job alone and C days for C to complete the job alone.
A and B can do a job in 6 days. They complete 1/6 th of the job in a day. i.e.  -- (1)
Similarly, B and C will complete 1/10th of the job in a day. i.e  -- (2)
And C and A will complete 1/7.5 or 2/15th of the job in a day i.e  -- (3).
Adding (1), (2) and (3) we get 
==>  or  . i.e working together, A, B and C complete 1/5th of the job in a day. Therefore, they will complete the job in 5 days.
Question 2
Subtracting eqn (2) from eqn (1) we get  --- (4)
Adding eqn (4) and eqn (3) we get,  or  . i.e. A does 1/10 of the job in a day and therefore, will take 10 days to complete the job working alone.
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