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.
Rate/Work Problem 2
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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
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
- misterholmes
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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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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'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?
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
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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