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A and B together can do a peace of work in 12 days, which B and C toge

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 60480
A and B together can do a peace of work in 12 days, which B and C toge  [#permalink]

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New post 26 Nov 2018, 02:07
2
8
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (02:53) correct 42% (02:49) wrong based on 74 sessions

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Intern
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B
Joined: 06 Apr 2018
Posts: 15
Location: India
WE: Information Technology (Computer Software)
Re: A and B together can do a peace of work in 12 days, which B and C toge  [#permalink]

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New post 26 Nov 2018, 04:09
13
1
Let's take total work needs to be done is 48 units (LCM of 12 and 16).

Given
A+B can do a 48 units work in 12 days.
In 1 day A+B can do 4 units of work.

B+C can do 48 units of work in 16 days
In 1 day B+C can do 3 units of work.

From question,

5A+7B+13C = 48.

5(A+B)+2B+2C+11C = 48.

5(A+B)+2(B+C)+11 = 48.

5x4+2x3+11C=48.

C = 2 units for 1 day.

So,48 units of work C will take 24 days.

Ans:-E
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Manager
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Joined: 25 Nov 2019
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Re: A and B together can do a peace of work in 12 days, which B and C toge  [#permalink]

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New post 09 Dec 2019, 15:42
Practical approach
A+B do the work alone in 12 days
A+B in 5 days is less than 1/2 done
C takes 13 days to do a little more than 1/2
~26 days for half is close enough to 24 and way to far from 21. 24 E is the answer very quickly

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Intern
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Joined: 08 Nov 2019
Posts: 3
GMAT 1: 580 Q47 V22
Re: A and B together can do a peace of work in 12 days, which B and C toge  [#permalink]

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New post 12 Dec 2019, 09:49
Hi,

I am not clear how to solve. can i get a better solution please ?

K
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Re: A and B together can do a peace of work in 12 days, which B and C toge  [#permalink]

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New post 29 Dec 2019, 23:52
1
mehro023 wrote:
Hi,

I am not clear how to solve. can i get a better solution please ?

K


A and B together can do a peace of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 Days and B for 7 Days, C finishes in 13 days. In how many days C alone will do the work?

A. 13
B. 17
C. 19
D. 21
E. 24

A and B together can do a piece of work in 12 days => A+B =1/12 (1)
B and C together can do in 16 days => B+C=1/16 (2)
After A has been working at it for 5 Days and B for 7 Days, C finishes in 13 days => 5A+7B+13C = 1 (3)
In how many days C alone will do the work? => C=?

3 variables & 3 equations so solve C using the equations:
A+B =1/12 (1) => A=1/12 - B (4)
B+C=1/16 (2) => C=1/16-B (5)

Sub (4) & (5) into (3):
5(1/12 - B) +7B + 13(1/16-B) =1
B=1/48

Sub B=1/48 into (5):
C=1/16 - 1/48
C=1/24
GMAT Club Bot
Re: A and B together can do a peace of work in 12 days, which B and C toge   [#permalink] 29 Dec 2019, 23:52
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A and B together can do a peace of work in 12 days, which B and C toge

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