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# Working together, A and B can do a job in 6 days. B and C can do the

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Math Expert
Joined: 02 Sep 2009
Posts: 65187
Working together, A and B can do a job in 6 days. B and C can do the  [#permalink]

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13 Sep 2019, 05:04
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Difficulty:

25% (medium)

Question Stats:

77% (02:17) correct 23% (02:23) wrong based on 69 sessions

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Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

(A) 8 days
(B) 7 days
(C) 6 days
(D) 5 days
(e) 3 days

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Concentration: Sustainability, Marketing
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Re: Working together, A and B can do a job in 6 days. B and C can do the  [#permalink]

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13 Sep 2019, 09:03
1
Bunuel wrote:
Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

(A) 8 days
(B) 7 days
(C) 6 days
(D) 5 days
(e) 3 days

given 1/a+1/b=1/6
1/b+1/c=1/10
1/c+1/a=1/7.5 ; 7.5 = 10/75 ; 2/15
find
1/a+1/b+1/a+1/c+1/b+1/c = 1/6+1/10+2/15
2/a+2/b+2/c=5+3+4/30
1/a+1/b+1/c= 6/30 ; 1/5 ; 5 hrs
IMO D
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Re: Working together, A and B can do a job in 6 days. B and C can do the  [#permalink]

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13 Sep 2019, 10:00
3
Bunuel wrote:
Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

(A) 8 days
(B) 7 days
(C) 6 days
(D) 5 days
(e) 3 days

Let the total work be 450 units...

So, Efficiency of A + B is 75 ; Efficiency of B + C is 45 & Efficiency of C + A is 60

Total efficiency of A + B + C is $$\frac{75 + 45 + 60}{2} = 90$$

So, Time taken by A , B & C to complete the work is 450/90 = 5 days, Answer must be (D)
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Abhishek....

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Intern
Joined: 29 Aug 2018
Posts: 29
Re: Working together, A and B can do a job in 6 days. B and C can do the  [#permalink]

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01 Jun 2020, 11:15
Abhishek009

Can you please explain how you assume 450? And why you divided by 2 at the end?

This method looks really useful; please explain
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Joined: 18 Dec 2017
Posts: 299
Re: Working together, A and B can do a job in 6 days. B and C can do the  [#permalink]

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01 Jun 2020, 18:13
Let the total job = 30 units( LCM of 6,10 and 7.5)
A and B efficiency =5 units/day
B and C efficiency =3 units/day
C and A efficiency =4 units/ day
2(A,B and C) efficiency = 5+4+3 =12
Therefore A,B and C efficiency= 6 units/day
Time =30/6= 5 days

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Re: Working together, A and B can do a job in 6 days. B and C can do the   [#permalink] 01 Jun 2020, 18:13