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A and B completed a work together in 5 days. Had A worked at twice the

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Bunuel
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A and B completed a work together in 5 days. Had A worked at twice the [#permalink] New post   07 Jan 2020, 07:13
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A and B completed a work together in 5 days. Had A worked at twice the speed and B at half the speed, it would have taken them only 4 days to finish the work. How much time would A take to finish the work if he worked alone?

A. 5
B. 6
C. 8
D. 9
E. 10
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E
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Re: A and B completed a work together in 5 days. Had A worked at twice the [#permalink] New post   13 Jan 2020, 05:28
Rate of A = a, Rate of B = b
a + b = 1/5 …………….(1)
2a + b/2 = ¼………….(2)

Calculating from statements (1) and (2),
b = 10(E)
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A and B completed a work together in 5 days. Had A worked at twice the [#permalink] New post   13 Jan 2020, 05:36
Option E

A system of equations:
\(\frac{1}{A}+\frac{1}{B}=\frac{1}{5}\)
\(2*\frac{1}{A}+\frac{1}{2}*\frac{1}{B}=\frac{1}{4}\)

Will lead to the following answers:
\(A=10\)
\(B=10\)

Thus, it would take A about 10 days to conclude the project by itself
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Re: A and B completed a work together in 5 days. Had A worked at twice the [#permalink] New post   13 Jan 2020, 07:31
Bunuel wrote:
A and B completed a work together in 5 days. Had A worked at twice the speed and B at half the speed, it would have taken them only 4 days to finish the work. How much time would A take to finish the work if he worked alone?

A. 5
B. 6
C. 8
D. 9
E. 10


Let original efficiency of A = a & Efficiency of B = 2b

Then total work, 5a + 10b

Again let changed efficiency of A = 2a & Efficiency of B = b

Then total work, 8a + 4b

Now, 5a + 10b = 8a + 4b

Or, 3a = 6b

Or, a = 2b

Now, the total work is 5*2b + 10b = 20b

Time required by A to complete the work alone is 20b/2b = 10 days, Answer must be (E)
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Re: A and B completed a work together in 5 days. Had A worked at twice the [#permalink] New post   06 Jan 2021, 07:52
A + B = 20%............(1)
Also 2A + B/2 = 25%
=> 4A + B = 50%
Using value from (1), 4A + 20% - A = 50%
=> 3A = 30% => A = 10%
Hence A alone will take 10 days by doing 10% per day.

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A and B completed a work together in 5 days. Had A worked at twice the [#permalink] New post   14 Jan 2021, 00:08
Using A=RT

A = (ra + rb)5 .... original
A = (2ra + 0.5rb)4 .... new

Set these two equations equal to each other since they're finishing the same amount of work in both situations:
5ra + 5rb = 8ra + 2rb .... 3rb = 3ra

So they work at the same rate originally, that means both of them would finish 1/5 of the job per day
Therefore, 'a' individually would finish 1/10 of the job per day -> it would take 'a' (E) 10 days to finish
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A and B completed a work together in 5 days. Had A worked at twice the [#permalink]
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