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# When they work alone, B needs 25% more time to finish a job than A

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Manager
Joined: 01 Nov 2017
Posts: 67
Location: India
When they work alone, B needs 25% more time to finish a job than A  [#permalink]

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28 Feb 2019, 23:19
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Difficulty:

55% (hard)

Question Stats:

57% (03:05) correct 43% (02:58) wrong based on 23 sessions

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When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?
(A) 20
(B) 16
(C) 22
(D) 18
(E) 24
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Joined: 02 Aug 2009
Posts: 7971
Re: When they work alone, B needs 25% more time to finish a job than A  [#permalink]

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01 Mar 2019, 01:13
raghavrf wrote:
When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?
(A) 20
(B) 16
(C) 22
(D) 18
(E) 24

Let A take 4x, so B takes 5x from ratio A:B=1:1.25.
Now let us convert each portion as an equation..

A works alone till half the job is done, so time taken is 2x,

then A and B work together for four days, so 4 days

finally B works alone to complete the remaining 5% of the job, so if B does 100% work in 5x days, B will do 5% in 5x*$$\frac{5}{100}=\frac{x}{4}$$

Thus, total time = $$2x+4+\frac{x}{4}=13......\frac{9x}{4}=9....x=4$$

B takes 5x or 5*4=20 days

A
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When they work alone, B needs 25% more time to finish a job than A  [#permalink]

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01 Mar 2019, 02:52
raghavrf wrote:
When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

(A) 20
(B) 16
(C) 22
(D) 18
(E) 24

Since B needs 25% more time to finish a job than A, B will do $$\frac{4}{9}$$th of the work if both A and B work together.

Let the total work be $$x$$.
If A finishes half the work to begin with, the work that remains is $$\frac{x}{2}$$. Also, B does 5% or $$\frac{x}{20}$$ of the work alone.

In 4 days both A and B do $$\frac{x}{2} - \frac{x}{20} = \frac{9x}{20}$$ of the work. In 1 day, they will do $$\frac{9x}{80}$$ of the work together.

In 1 day, B will do $$\frac{4}{9}*\frac{9x}{80}= \frac{x}{20}$$ of the work.

Therefore, B, working alone, can complete the work in 20(Option A) days.
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Re: When they work alone, B needs 25% more time to finish a job than A  [#permalink]

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03 Mar 2019, 04:30
raghavrf wrote:
When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?
(A) 20
(B) 16
(C) 22
(D) 18
(E) 24

let the rate of work of A =4x
and rate of B ; 1.25 of rate of a ; 5x

given
half job done by A ; i.e 2 hrs ; 2x
working together they complete work in 4 days
and B working alone completes 5% of remaining work at rate of 5x ; 5/100 * 5x= 25x/100; x/4

13 = 4+x/4+2x
solve for x = 4
so total time taken by b = 5x 5*4 ; 20 days
IMO A
Re: When they work alone, B needs 25% more time to finish a job than A   [#permalink] 03 Mar 2019, 04:30
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