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# A takes half as long as B takes to do a piece of work, C does it in t

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Intern
Joined: 03 Nov 2019
Posts: 43
A takes half as long as B takes to do a piece of work, C does it in t  [#permalink]

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26 Nov 2019, 11:46
3
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Difficulty:

45% (medium)

Question Stats:

67% (02:54) correct 33% (02:29) wrong based on 33 sessions

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A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined
VP
Joined: 19 Oct 2018
Posts: 1171
Location: India
Re: A takes half as long as B takes to do a piece of work, C does it in t  [#permalink]

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26 Nov 2019, 11:55
Efficiency of A =2x

Efficiency of B = x

Efficiency of C= 3x

Time taken by A= $$\frac{7*(3x+2x+x)}{2x}$$=21

Time taken by B= $$\frac{7*(3x+2x+x)}{x}$$=42

Time taken by C=$$\frac{ 7*(3x+2x+x)}{3x}$$=14

Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined
VP
Joined: 20 Jul 2017
Posts: 1145
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: A takes half as long as B takes to do a piece of work, C does it in t  [#permalink]

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27 Nov 2019, 09:50
1
Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined

Let the time taken by A = t
—> Time taken by B = 2t &
Time taken by C = 2t*t/(2t + t) = 2t/3

working together they can complete 7 days
—> 1/t + 1/2t + 3/2t = 1/7
—> 3/t = 1/7
—> t = 21 days

A = t = 21
B = 2t = 42
C = 2t/3 = 2/3*21 = 14

Posted from my mobile device
Director
Joined: 18 Dec 2017
Posts: 853
Location: United States (KS)
Re: A takes half as long as B takes to do a piece of work, C does it in t  [#permalink]

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27 Nov 2019, 09:50
Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined

Well, A takes half as long as B.

So Option C is gone.

C take as long as A&B together.

Option A works.
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Intern
Joined: 24 Nov 2019
Posts: 4
Re: A takes half as long as B takes to do a piece of work, C does it in t  [#permalink]

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01 Dec 2019, 05:59
Dillesh4096 wrote:
Ansh777 wrote:
A takes half as long as B takes to do a piece of work, C does it in the same time as A and B together, and if all three work together they would take 7 days, how long would each take separately?
A) 21 days, 42 days, 14days
B) 20days, 40 days, 40/3 days
C) 15 days, 45 days, 45/4 days
D) None of these
E) Cannot be determined

Let the time taken by A = t
—> Time taken by B = 2t &
Time taken by C = 2t*t/(2t + t) = 2t/3

working together they can complete 7 days
—> 1/t + 1/2t + 3/2t = 1/7
—> 3/t = 1/7
—> t = 21 days

A = t = 21
B = 2t = 42
C = 2t/3 = 2/3*21 = 14

Posted from my mobile device

Can you plz explain how did u find this 'Time taken by C = 2t*t/(2t + t) = 2t/3' ?
Re: A takes half as long as B takes to do a piece of work, C does it in t   [#permalink] 01 Dec 2019, 05:59
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