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A is 20% more efficient than B and takes 40 days less

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A is 20% more efficient than B and takes 40 days less  [#permalink]

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New post 16 Jul 2017, 05:49
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Question Stats:

83% (03:05) correct 17% (00:49) wrong based on 12 sessions

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A is 20% more efficient than B and takes 40 days less than B to complete a job. B is 50% more efficient than C. On this job, A works for 50 days and quits. Then B takes over and works for 120 days & quits. C completed the remaining work. The no. of days worked by C is

A) 90
B) 120
C) 240
D) 150
E) 360

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A is 20% more efficient than B and takes 40 days less  [#permalink]

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New post 16 Jul 2017, 06:44
Quite interesting question. I took lot of time to solve it. Did it by mathematical approach.

Let the efficiency of A, B and C be denoted by a, b and c

\(a = (1+\frac{1}{5})*b => a = \frac{6}{5} b => \frac{a}{b} = \frac{6}{5}\) <----- Also means (Rate of A) : (Rate of B) = 6:5

Let Rate of A = 6x and Rate of B = 5x. Since both do same work, let it be denoted by 1. Make an RTW chart with this data (See attached) to keep track of all the information.

A takes 40 days less than B. From RTW chart we get

\(\frac{1}{5x} - \frac{1}{6x} = 40\)

Solving for x we get \(x = \frac{1}{1200}\)

Put this back in RTW chart

B is 50% more efficient than C. b = \((1+\frac{1}{2}) c => b = \frac{3}{2} c => c = b*\frac{2}{3}\)

Substuting the Rate of B (Already got above) we get Rate of \(C = \frac{1}{360}\)

We now have all the rates.

A works for 50 days. Means A does 1/4 of the work.
B works for 120 days. Means B does 1/2 of the work. Total work completed by A and B = 1/4 + 1/2 = 3/4. Remaining work = 1/4
Remaining work done by C. This means C works for 90 days to complete the work.

Final answer = A


I hope this helps!


theperfectgentleman wrote:
A is 20% more efficient than B and takes 40 days less than B to complete a job. B is 50% more efficient than C. On this job, A works for 50 days and quits. Then B takes over and works for 120 days & quits. C completed the remaining work. The no. of days worked by C is

A) 90
B) 120
C) 240
D) 150
E) 360

Attachments

GMC RTW QUESTION.png
GMC RTW QUESTION.png [ 33.85 KiB | Viewed 10904 times ]


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A is 20% more efficient than B and takes 40 days less  [#permalink]

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New post 16 Jul 2017, 07:12
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theperfectgentleman wrote:
A is 20% more efficient than B and takes 40 days less than B to complete a job. B is 50% more efficient than C. On this job, A works for 50 days and quits. Then B takes over and works for 120 days & quits. C completed the remaining work. The no. of days worked by C is

A) 90
B) 120
C) 240
D) 150
E) 360


I'm assuming rate of work of A,B and C!
Let the rate of work of C to be 100 units/day
Since B is 50% more efficient than C, B's rate of work is 150 units/day
Since A is 20% more than B, A's rate of work is 180 units/day

It is said that the days A takes to complete the work is 40 days lesser than B,
Let the total number of days B does the work in be x
180(x-40) = 150x
30x = 180*40 => x=240
Total work is 150x = 36000 units

Since A works for 50 days and quits, A does 50*180 = 9000 units
B works for 120 days, B does 120*150 = 18000 units, leaving 36000 - (9000+18000) or 9000 units for C to do.

As C does 100 units of work in a day, he would take 90 days to complete the remaining 9000 units.(Option A)
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Re: A is 20% more efficient than B and takes 40 days less  [#permalink]

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New post 16 Jul 2017, 08:02
theperfectgentleman wrote:
A is 20% more efficient than B and takes 40 days less than B to complete a job. B is 50% more efficient than C. On this job, A works for 50 days and quits. Then B takes over and works for 120 days & quits. C completed the remaining work. The no. of days worked by C is

A) 90
B) 120
C) 240
D) 150
E) 360



hi..

a slightly faster ad logical way would be

A is 20% more efficient than B and takes 40 days less than B to complete a job. ....
A will take 100/120 th of time that B takes... so \(b-\frac{100}{120}b=\frac{b}{6}=40\)
OR B takes 40*6=240 days to complete and A takes 240-40=200 days

B is 50% more efficient than C.

so \(c=\frac{3}{2}b=360days\)...

lets solve the Q now...
A works for 50 days and quits. EQUIVALENT to \(50*\frac{6}{5}=60 days of B\)

Then B takes over and works for 120 days & quits. .. so total days of B is 120+60=180

C completed the remaining work. ...
remaining work is \(1-\frac{180}{240}=\frac{1}{4}\)
Now C takes 360 to do FULL work so C will take \(360*\frac{1}{6}\) or 90 days to complete \(\frac{1}{6}\) of work..

ans A
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Re: A is 20% more efficient than B and takes 40 days less  [#permalink]

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New post 16 Jul 2017, 08:47
1
theperfectgentleman wrote:
A is 20% more efficient than B and takes 40 days less than B to complete a job. B is 50% more efficient than C. On this job, A works for 50 days and quits. Then B takes over and works for 120 days & quits. C completed the remaining work. The no. of days worked by C is

A) 90
B) 120
C) 240
D) 150
E) 360


\(A = 1.2B = 1.8C\)
\(B = 1.5C\)
\(C = ?\)

\(A = 1.2B = 6B/5\)
\(B - 5B/6 = 40\)
\(6B - 5B/6 = 40\)
\(B = 240\)

So, \(A = 240 - 40 = 200\), and \(C = 240*1.5 = 360\).

Work done by \(A\) in \(50\) days = \(\frac{50}{200} = \frac{1}{4}\)
Work done by \(B\) in \(120\) days = \(\frac{120}{240} = \frac{1}{2}\)

So, we have: \(\frac{1}{4} + \frac{1}{2} + \frac{n}{360} = 1\)
\(\frac{n}{360} = 1 - \frac{3}{4}\)
\(\frac{n}{360} = \frac{1}{4}\)
\(n = \frac{360}{4} = 90\). Ans - A.
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Re: A is 20% more efficient than B and takes 40 days less  [#permalink]

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New post 16 Jul 2017, 11:04
theperfectgentleman wrote:
A is 20% more efficient than B and takes 40 days less than B to complete a job. B is 50% more efficient than C. On this job, A works for 50 days and quits. Then B takes over and works for 120 days & quits. C completed the remaining work. The no. of days worked by C is

A) 90
B) 120
C) 240
D) 150
E) 360


let b=B's time to do job alone
b-40=A's time to do job alone
[1/(b-40)]/(1/b)=1.2/1
b=240 hours
b-40=200 hours
50*(1/200)+120*(1/240)=3/4 of job
C's time to do job alone=(3/2)(240)=360 hours
let c=C's time to finish job
c*(1/360)=1/4 of job remaining
c=90 hours
A

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
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Re: A is 20% more efficient than B and takes 40 days less   [#permalink] 16 Jul 2017, 11:04
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