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

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Intern
Joined: 01 Jan 2016
Posts: 28
A is 20% more efficient than B and takes 40 days less  [#permalink]

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16 Jul 2017, 05:49
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Difficulty:

45% (medium)

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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WE: Sales (Telecommunications)
A is 20% more efficient than B and takes 40 days less  [#permalink]

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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.

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 [ 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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16 Jul 2017, 07:12
2
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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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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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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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!

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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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