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by ultrasound » Wed Jul 06, 2016 8:53 am
A is 80% as efficient as B. C does two-third of the work done by A and B together in the same time. If C alone does the work in 10 Days. Then A and C, together can do the work in........
(A) 12 days (B) 24 days
(C) 18 days (D) 6 Days

plz help me i m stuck in this question..
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by GMATGuruNY » Wed Jul 06, 2016 10:06 am
ultrasound wrote:A is 80% as efficient as B. C does two-third of the work done by A and B together in the same time. If C alone does the work in 10 Days. Then A and C, together can do the work in........
(A) 12 days (B) 24 days
(C) 18 days (D) 6 Days

plz help me i m stuck in this question..
Let B's rate = 15 widgets per day.
Since A is 80% as efficient as B, A's rate = (80/100)(15) = (4/5)(15) = 12 widgets per day.

Combined rate for A and B = 15+12 = 27 widgets per day.
Since C does two-thirds of the work done by A and B, C's rate = (2/3)(27) = 18 widgets per day.
Since C completes the job in 10 days, the total job = (C's rate)(C's time) = (18)(10) = 180 widgets.

Combined rate for A and C = 12+18 = 30 widgets per day.
Time for A and C together to produce 180 widgets = w/r = 180/30 = 6 days.

The correct answer is D.
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by Matt@VeritasPrep » Thu Jul 07, 2016 3:03 pm
Let's get the rates first.

C = 1/10 per day
C = (2/3)(A + B), so (A + B) = 3/20
A = (4/5)B, so A + (5/4)A = 3/20, and A = 1/15 per day

A + C = 1/10 + 1/15 = 1/6, so they'll do the job in 6 days.
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by Matt@VeritasPrep » Thu Jul 07, 2016 3:04 pm
That said, there is a SCREAMINGLY easy answer hidden right in front of us!

Since C alone can do the work in 10 days, A + C must be less than 10 days.

Only D is less than 10 days, so we're done ... in five seconds. :D
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by OptimusPrep » Thu Jul 14, 2016 11:01 pm
ultrasound wrote:A is 80% as efficient as B. C does two-third of the work done by A and B together in the same time. If C alone does the work in 10 Days. Then A and C, together can do the work in........
(A) 12 days (B) 24 days
(C) 18 days (D) 6 Days

plz help me i m stuck in this question..
Assume the work rate B = B units/hour
Work rate of A = 0.8B units/hour

Work done by A and C together = 1.8B
Hence the work rate of C = 2/3*1.8B = 1.2B units/hour

Time taken by C alone = 10 days.
Hence total units of work = 1.2B*10 = 12B

Time taken by A and C together = 12B/2B = 6 days

Correct Option: D
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