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by vaibhav101 » Sun Jun 03, 2018 9:47 am

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Answers

A

B

C

D

E

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Difficulty—

2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these
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by GMATGuruNY » Sun Jun 03, 2018 11:42 am
vaibhav101 wrote:2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these
Let the job = 15 units.

Since A and B take 5 days to produce the 15-unit job, A+B = w/t = 15/5 = 3 units per day.
Thus:
A+B = 3.

Since 2A and (1/3)B take 3 days to produce the 15-unit job, 2A + (1/3)B = w/t = 15/3 = 5 units per day.
Thus:
2A + (1/3)B = 5
6A + B = 15.

Subtracting the red equation from the blue equation, we get:
(6A + B) - (A+B) = 15 - 3
5A = 12
A = 12/5 units per day.

Since A's rate = 12/5 units per day, the time for A alone to produce the 15-unit job = 15/(12/5) = 75/12 = 25/4 days.

The correct answer is B.
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by Scott@TargetTestPrep » Tue Jun 05, 2018 9:38 am
vaibhav101 wrote:2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these
The rate of A is 1/A and the rate of B is 1/B.

If A works twice as efficiently, the new rate is 1/A x 2 = 2/A

The new rate of B is 1/3 x 1/B = 1/(3B)

So we have two equations:

1/A + 1/B = 1/5

Multiplying by 2, we have:

2/A + 2/B = 2/5

and

2/A + 1/(3B) = 1/3

Subtracting the 2nd equation from the first, we have:

2/B - 1/(3B) = 2/5 - 1/3

Multiplying by 15B, we have:

30 - 5 = 6B - 5B

25 = B

Let's now determine A:

1/A + 1/25 = 1/5

Multiplying by 25A, we have:

25 + A = 5A

25 = 4A

25/4= A

Answer: B

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