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

Question

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

PareshGmat · Accepted Answer

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?

BassanioGratiano · Answer

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.

xserenity114 · Answer

I'm a little confused too. I got 4 days :\ Will wait for solution to see where I went wrong.

pate13 · Answer

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.

sushmimadhu · Answer

I got 4 days. How the answer is 16 days? Can someone please explain?

jayanth7290 · Answer

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

BassanioGratiano · Answer

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.

jayanth7290 · Answer

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 ?

LUC999 · Answer

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. 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

KarishmaB · Answer

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.

pacifist85 · Answer

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.

Nunuboy1994 · Answer

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.

Bunuel · Answer

The difficulty level is calculated automatically based on the timer stats from the users which attempted the question.

ScottTargetTestPrep · Answer

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

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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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