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Math Expert V
Joined: 02 Sep 2009
Posts: 58415
A, B and C can do a work in 6, 8, 12 days respectively. B and C work t  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 42% (01:43) correct 58% (01:49) wrong based on 81 sessions

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A, B and C can do a work in 6, 8, 12 days respectively. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?

A. 2 days
B. 3 days
C. 4 days
D. 5 days
E. 6 days

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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: A, B and C can do a work in 6, 8, 12 days respectively. B and C work t  [#permalink]

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2
2
Total work to be done = LCM(6,8,12) = 24 units
A can do 4 units per day
B can do 3 units per day
C can do 2 units per day

B+C in 1 day = 5 units
for 2 days, 10 units will be completed by B and C.
Remaining is 14 units.
Now A and B work together, They can do 4+3 = 7 units per day.
Then 14 units will be completed in 2 days.

A is the answer.
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VP  D
Joined: 31 Oct 2013
Posts: 1464
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: A, B and C can do a work in 6, 8, 12 days respectively. B and C work t  [#permalink]

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Bunuel wrote:
A, B and C can do a work in 6, 8, 12 days respectively. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?

A. 2 days
B. 3 days
C. 4 days
D. 5 days
E. 6 days

LCM method is suitable here.

LCM of 6,8,12 =24 units of work.

A's work = 4 units /day
B's work = 3 units/days
C's work = 2 units/day

(A + C)' 2 days work = 3 +2 = 5 *2 = 10 units.

Remaining Work = 24 - 10 = 14

14 Units done by (A + B)

(A + B)'s performance in a day = 4 + 3 =7

14/7 = 2 days.

Thus, A and B will take only 2 days to finish the remaining work .

A is the correct answer.
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5014
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
A, B and C can do a work in 6, 8, 12 days respectively. B and C work t  [#permalink]

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Bunuel wrote:
A, B and C can do a work in 6, 8, 12 days respectively. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?

A. 2 days
B. 3 days
C. 4 days
D. 5 days
E. 6 days

rate of B & C = 1/8 + 1/12 ; 5/24
so amount of work done by b & c = 5/24 * 2 = 5/12
work left = 1-5/12 = 7/12

rate of work of A & B = 1/6+ 1/8 = 7/24
since
w=r*t
w=7/12 , r = 7/24
t = 24/12 = 2

total work would be finished in 2 days of B& C and 2 days of A & B = 2+2 = 4
IMO C
Manager  S
Joined: 19 Jan 2019
Posts: 88
Re: A, B and C can do a work in 6, 8, 12 days respectively. B and C work t  [#permalink]

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I just have one doubt... Is the question asking the total number of days or just the days in which A&b finish the remaining work. If it was total number of days then the answer is 4 days .
If the question is asking only the number of days it took A&b to finish the remaining work then the answer is 2 days ..... Which one is the right one. As far as I understood the question, it's asking about the days A&b finished the work, but OA is C..
Can anyone clear my doubt..

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GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5014
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A, B and C can do a work in 6, 8, 12 days respectively. B and C work t  [#permalink]

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thyagi wrote:
I just have one doubt... Is the question asking the total number of days or just the days in which A&b finish the remaining work. If it was total number of days then the answer is 4 days .
If the question is asking only the number of days it took A&b to finish the remaining work then the answer is 2 days ..... Which one is the right one. As far as I understood the question, it's asking about the days A&b finished the work, but OA is C..
Can anyone clear my doubt..

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thyagi
question has asked How long will it take to finish the work?

which means total days..
Intern  B
Joined: 20 Nov 2018
Posts: 27
Location: India
A, B and C can do a work in 6, 8, 12 days respectively. B and C work t  [#permalink]

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Bunuel wrote:
A, B and C can do a work in 6, 8, 12 days respectively. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?

A. 2 days
B. 3 days
C. 4 days
D. 5 days
E. 6 days

if given n people finishing a work in k days
1/a + 1/b + 1/c + 1/d + .... + 1/n= 1/k (i.e., 1/k th fraction of work done on each day)

given :
1/a = 1/6
1/b = 1/8
1/c = 1/12

b and c work together for two days
each day 1/b+1/c
two days 2*(1/b+1/c)

a replaces c
a and b works for say t days

t*(1/a+1/b)

the sum all the fractions work done should be one
2*(1/b+1/c) + t*(1/a+1/b) = 1

2*(1/8 + 1/12) + t*(1/6+1/8) = 1
1/4+1/6+7t/24 = 1
5/12 + 7t/24 = 1
7t/24 = 1- 5/12 = 7/12
t = 2 days
if the question is asking about the amount of time taken to finish the work after A replaces C
Option A - 2 days
if the question is asking for the total time taken to finish the work
2 + 2 = 4 days
Option C - 4 days

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please leave a kudos  A, B and C can do a work in 6, 8, 12 days respectively. B and C work t   [#permalink] 14 Feb 2019, 11:20
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