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Rate/Work Problem 2

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Rate/Work Problem 2

by knight247 » Thu Mar 14, 2013 11:45 pm
A, B and C need a certain unique time to do a certain work. C needs 1 hours less than A to complete the work. Working together, they require 30 minutes to complete 50% of the job. The work also gets completed if A and B start working together and A leaves after 1 hour and B works for a further 3 hours. How much work does C do per hour?

(A)16.66%
(B)33.33%
(C)50%
(D)66.66%
(E)None of these

OA - B

I would appreciate a direct solution to this problem using equations only, as I've already figured out the backdoor method to solving this problem.
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by neha24 » Fri Mar 15, 2013 12:11 am
are u sure answer is B ?
as per me it sud be 50 %

also i didnt find the language of this question particularly gmat types !!
question stem says :C needs 1 hours less than A to complete the work. Working together, they require 30 minutes to complete 50% of the job

working together is seeming to modify just the working of C and A together !!!
plz share the source and answer so as i may write the solution
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by misterholmes » Fri Mar 15, 2013 8:37 am
The sentence "Working together" is misplaced, for sure. It should precede the sentence about a and c. Otherwise we would have a and c doing the job in 1 hour, and THAT is inconsistent with c doing the job 1 hour faster than a.
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by Anju@Gurome » Fri Mar 15, 2013 10:26 am
knight247 wrote:A, B and C need a certain unique time to do a certain work. C needs 1 hours less than A to complete the work. Working together, they require 30 minutes to complete 50% of the job. The work also gets completed if A and B start working together and A leaves after 1 hour and B works for a further 3 hours. How much work does C do per hour?
As others have pointed out this line seems misplaced. This should be the second line not third. If it is the third line, then it means A and C together requires 1 hour to finish the job. Which is not impossible as misterholmes mentioned but the answer will be an irrational number, i.e. 'None of these'

If it is the second line, then it means a, b, and c together requires 1 hour to finish the job.

Let us assume, they take A, B, and C hours to finish the job individually, respectively.
Hence, (1/a + 1/b + 1/c) = 1
Also, a = (c + 1) ----> 1/a = 1/(c + 1)
And, (1/a + 4/b) = 1 ----> 1/b = (1 - 1/a)/4 = (1 - 1/(c + 1))/4 = c/(4*(c + 1))

Replacing these values of 1/a and 1/b in the first equation,
  • --> 1/(c + 1) + c/(4*(c + 1)) + 1/c = 1
    --> [4c + c² + 4(c + 1)]/[4*c*(c + 1)] = 1
    --> c² + 8c + 4 = 4c² + 4c
    --> 3c² - 4c - 4 = 0
    --> 3c² - 6c + 2c - 4 = 0
    --> (c - 2)(3c + 2) = 0
As C cannot be negative, c = 2

In one hour, C does 1/c of the work, i.e. 1/2 of the work.

The correct answer is C.
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