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Time taken by A to complete a job is 6 days. Time taken by B to comple

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raj44
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Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   Updated on: 15 Dec 2014, 06:48
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Time taken by A to complete a job is 6 days. Time taken by B to complete the same job is 12 days. They start working together and work for 2 days. B then leaves and A is left alone to complete the job. In how many days will A finish the remaining work, if it is given that A’s efficiency decreases by 25 percent after B left?

A. 16
B. 14
C. 12
D. 10
E. 4
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E

Originally posted by raj44 on 12 Dec 2014, 07:13.
Last edited by Bunuel on 15 Dec 2014, 06:48, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   14 Dec 2014, 21:29
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raj44 wrote:
Time taken by A to complete a job is 6 days. Time taken by B to complete the same job is 12 days. They start working together and work for 2 days. B then leaves and A is left alone to complete the job. In how many days will A finish the remaining work, if it is given that A’s efficiency decreases by 25 percent after B left?

A. 8
B. 10
C. 12
D. 14
E. 16


Answer = 4 days

Rate of A \(= \frac{1}{6}\)

Rate of B \(= \frac{1}{12}\)

Combined rate \(= \frac{1}{12} + \frac{1}{6} = \frac{3}{12} = \frac{1}{4}\)

Combined work done in 2 days \(= \frac{1}{4} * 2 = \frac{1}{2}\)

Remaining work \(= 1 - \frac{1}{2} = \frac{1}{2}\)

Efficiency of A decreases by 25% \(= \frac{1}{6} * \frac{3}{4} = \frac{1}{8}\)

Days required by A alone for remaining work \(= \frac{1}{2} * 8 = 4 days\)

Karishma / Bunuel : Kindly tell if the answer is correct?
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Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   Updated on: 26 Jan 2015, 10:08
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I have the suspicion that none of the answer choices are correct.

If it takes A six days to complete a job by itself, and B helps A for two days before leaving, how can it take more than six days to finish the job without B? Even if A is operating at 25% less efficiently it can't take more than 7.5 (6 days multiplied by 5/4) days to complete the job.

------------------

Thanks for editing the answer choices to include the actual answer.

A = 1/6
B = 1/12

If they are working together for 2 days then we need to find out much of the work is done before A starts working by itself.

A + B = x/2
1/6 + 1/12 = x/2
1/4 = x/2
x = 1/2

So together A and B have done half the work. This means that A will finish the other half of the work with a 25% inefficiency.

New Rate for A: 1/6 * 3/4 = 1/8

It would take A 8 days to finish the whole job by itself.

1/8 = 1/(2t)
t = 4

It would take 4 days for A to finish the job by itself.

Originally posted by BassanioGratiano on 12 Dec 2014, 11:23.
Last edited by BassanioGratiano on 26 Jan 2015, 10:08, edited 2 times in total.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   14 Dec 2014, 15:48
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Time taken by A to complete a job is 6 days. Time taken by B to complete the same job is 12 days. They start working together and work for 2 days. B then leaves and A is left alone to complete the job. In how many days will A finish the remaining work, if it is given that A’s efficiency decreases by 25 percent after B left?

A. 8
B. 10
C. 12
D. 14
E. 16


A and B work together for two days:RT=W==> (1/6+1/12)2=1/2
Now A has is left with another half work to complete.
Original Rate of A=1/6
Now when the rate is decreased by 25%==>it is decreased by 1/4==>3/4 of the original of the original i.e (3/4)(1/6)=3/24

A will finish the work in..RT=W==>(3/24)T=1/2==>T=4days..

Please let me know where am I going wrong
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   12 Dec 2014, 15:36
I'm a little confused too. I got 4 days :\ Will wait for solution to see where I went wrong.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   13 Dec 2014, 14:42
I also believe that none of the answer choices are correct. I got 4 days for the answer.

A = 1/6 or 2/12
B = 1/12

If they work together for 2 days, they complete 6/12 of the work: 2(1/12 + 2/12)

The remaining work is 6/12 of the job.

If A's efficiency decreases by 25%, s/he now works at a rate of 1.5/12.

A would complete the remaining work in 4 days: 1.5 * 4 = 6.

The answer is 4 days.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   13 Dec 2014, 15:20
I got 4 days. How the answer is 16 days? Can someone please explain?
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   13 Dec 2014, 16:04
sathishmadhu wrote:
I got 4 days. How the answer is 16 days? Can someone please explain?


Answer is 4 only probably some error in the options ..

SInce 50 % of work is done when b leaves in 2 days

Normally A can finish the 50 percent in 3 days but as they mentioned efficiency has been reduced by 25 % which means 3/4th of A's efficiency so he takes 4/3*3 days = 4 days
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   14 Dec 2014, 10:15
jayanth7290 wrote:
sathishmadhu wrote:
I got 4 days. How the answer is 16 days? Can someone please explain?


Answer is 4 only probably some error in the options ..

SInce 50 % of work is done when b leaves in 2 days

Normally A can finish the 50 percent in 3 days but as they mentioned efficiency has been reduced by 25 % which means 3/4th of A's efficiency so he takes 4/3*3 days = 4 days


Could you explain why we take the 3 days it would take a complete the last half of the job and multiply it by 4/3?

I would have thought that you'd take the 3 days and multiply it by 1.25 = 3.75.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   14 Dec 2014, 10:43
BassanioGratiano wrote:
jayanth7290 wrote:
sathishmadhu wrote:
I got 4 days. How the answer is 16 days? Can someone please explain?


Answer is 4 only probably some error in the options ..

SInce 50 % of work is done when b leaves in 2 days

Normally A can finish the 50 percent in 3 days but as they mentioned efficiency has been reduced by 25 % which means 3/4th of A's efficiency so he takes 4/3*3 days = 4 days


Could you explain why we take the 3 days it would take a complete the last half of the job and multiply it by 4/3?

I would have thought that you'd take the 3 days and multiply it by 1.25 = 3.75.


The point u need to consider here is efficiency is inversely proprtional to no of days

ex : A takes 5 days to complete the work

now if some one says he can work with 50 % efficiency due to some reasons then for total no of days : u multiply

with 2 but not 1.5 right ?

I multiplied the days (3) with 4/3 because efficiency was 3/4th (effciiency or unit work * no of days needs to b constant )

This applies for anything of the form ab = constant ( u can apply the same thing v * t = distance )..

I hope u got it ?
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   15 Dec 2014, 00:50
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raj44 wrote:
Time taken by A to complete a job is 6 days. Time taken by B to complete the same job is 12 days. They start working together and work for 2 days. B then leaves and A is left alone to complete the job. In how many days will A finish the remaining work, if it is given that A’s efficiency decreases by 25 percent after B left?

A. 8
B. 10
C. 12
D. 14
E. 16


Say the work is of 12 units.
A does 2 units a day alone.
B does 1 unit a day alone.

They work together for 2 days so they complete 2*3 units = 6 units of work.
6 units are remaining. A has to complete it alone.
But A's efficiency decreased by 25% i.e. he did only 1.5 units a day (a decrease of 25% in efficiency which is 2 units a day). So to complete 6 units, A takes 6/1.5 = 4 days

Correct answer is 4 days.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   16 Dec 2014, 08:30
EASY STEP BY STEP EXPLANATION:

1) Start by working out the individual rates:
A: 1/6 (1 work in 6 days)
B: 1/12 (I work in 12 days)

Normally, we need to find the amount of work in 1 day, so that we can find the amount of work for 2 days later on:
1 (work) in 6 (days)
X (work) in 1 (day)?
Of course, this still gives 1/6 in this case for A and 1/12 for B.

2) Together in 1 day they will do:
1/6+1/12=3/12
So, together in 2 days they will do:
3/12*(2)=6/12

3) This means that there is still 6/12 of the work to be done by A, that now has minus 25% of its capacity.
We calculate the new capacity: 1/6 - (0,25*1/6) = 1/6 - 0,25/6 = 0,75/6=(3/4)/(6/1)=3/24=1/8.

4) The 6/12 we found that were still left to do is simplified to 1/2.
Now, we use the formula R*T=W. The work is 1/2 and the rate is 1/8.
So, R*T=1/2 -> T=(1/2)/(1/8) -> T=8/2 -> T=4.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   16 Mar 2017, 03:22
Is this really a 500 level question? This seems like a low 600 question- I did get the answer right but it required it some thinking and paying close attention to what the question was asking.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   16 Mar 2017, 06:54
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Nunuboy1994 wrote:
Is this really a 500 level question? This seems like a low 600 question- I did get the answer right but it required it some thinking and paying close attention to what the question was asking.


The difficulty level is calculated automatically based on the timer stats from the users which attempted the question.
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   21 Mar 2017, 06:22
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raj44 wrote:
Time taken by A to complete a job is 6 days. Time taken by B to complete the same job is 12 days. They start working together and work for 2 days. B then leaves and A is left alone to complete the job. In how many days will A finish the remaining work, if it is given that A’s efficiency decreases by 25 percent after B left?

A. 16
B. 14
C. 12
D. 10
E. 4


Since it takes A 6 days to complete a job and B 12 days to complete a job, the rate of A is 1/6 and the rate of B is 1/12.

We are given that they start working together for 2 days and then A has to complete the job.

In two days, they complete (1/6)(2) + (1/12)(2) = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 of the job. Thus, A has to complete 1/2 of the job.

Since A’s rate decreases by 25%, the new rate of A is:

1/6 x 0.75 = 1/6 x 3/4 = 1/8

Thus, A will complete the job in (1/2)/(1/8) = 1/2 x 8 = 4 days.

Answer: E
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Re: Time taken by A to complete a job is 6 days. Time taken by B to comple [#permalink] New post   21 Sep 2020, 07:12
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