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# A, B and C can do a work in 6, 8, 12 days resp. B and C work

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Director
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A, B and C can do a work in 6, 8, 12 days resp. B and C work [#permalink]

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04 May 2006, 08:10
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A, B and C can do a work in 6, 8, 12 days resp. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?
Manager
Joined: 27 Jan 2006
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04 May 2006, 08:57
remgeo wrote:
A, B and C can do a work in 6, 8, 12 days resp. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?

Working spd per day.
a) 1/6
b) 1/8
c) 1/12

when b, c work together, their working speed is 1/8 + 1/12 = 20/96
because they worked for 2 days, 20/96 * 2 = 5/12

the left amount of work is 1-5/12=7/12

when a and c work together, spd is 1/6+1/12 = 1/4

(7/12) / (1/4) = 7/3
Manager
Joined: 29 Apr 2006
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04 May 2006, 09:04
4 days. This is based on A&B working for 2 consecutive days following the 2 days that B&c worked.
Work done by B&C = 2(B+C) = 2(1/8 + 1/12) = 5/12
Work done by A+B for 2 days = 2(A+B) = 2(1/6 +1/8) = 7/12

Total work = 5/12 +7/12 =1
Total days = 2 +2 = 4
Manager
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04 May 2006, 09:10
Question says that A takes the place of C. There we have the work done by A+B.

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

Working spd per day.
a) 1/6
b) 1/8
c) 1/12

when b, c work together, their working speed is 1/8 + 1/12 = 20/96
because they worked for 2 days, 20/96 * 2 = 5/12

the left amount of work is 1-5/12=7/12

when a and c work together, spd is 1/6+1/12 = 1/4

(7/12) / (1/4) = 7/3
VP
Joined: 29 Dec 2005
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04 May 2006, 09:15
remgeo wrote:
A, B and C can do a work in 6, 8, 12 days resp. B and C work together for 2 days and then A takes C's place. How long will it take to finish the work?

remaining work after 2 days of work by a and b = 1-2(1/12+1/8)=7/12
a and b can do 7/12 work in 2 days = (24/7)(7/12) = 2 days

so total days = 4 days
Manager
Joined: 13 Apr 2006
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04 May 2006, 09:40
to get amount finished in 2 days w/B & C: (1/8 + 1/12)*2=5/12

subtract from 1
i.e. 12/12 - 5/12 = 7/12

7/12 = (1/6*1/8)t
t=2

total days= 2 + 2=4
Manager
Joined: 27 Jan 2006
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04 May 2006, 09:53
i did silly mistake.
GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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05 May 2006, 03:00
A = 1/6 job per day
B = 1/8 job per day
C = 1/12 job per day

B+C = 1/8 + 1/12 = 5/24 job per day. They work for two days, so 7/12 job is left.

A+B = 1/6 + 1/8 = 7/24 job per day. The # of days to complete = 7/12 * 24/7 = 2 days.

Total = 2+2 = 4 days
Senior Manager
Joined: 29 Jun 2005
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05 May 2006, 04:09
Yes it is 4

A=w/6, B=w/8, C=w/12
B+C for 2 days = (w/8+w/12)*2=5w/12, so 7w/12 remains
A takes C place, thus (w/8+w/6)*x=7w/12  x=2
2+2=4
05 May 2006, 04:09
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