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# A and B together can complete one-ninth of a job in a day.

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A and B together can complete one-ninth of a job in a day. [#permalink]  24 Jul 2013, 18:25
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A and B together can complete one-ninth of a job in a day. What is the difference between the maximum and minimum number of days A could take to complete the job alone, if A and B take whole number of days to complete the job alone?

A 45
B.60
C.80
D.90
E.Cannot be determined
[Reveal] Spoiler: OA

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Re: A and B together can complete one-ninth of a job in a day. [#permalink]  24 Jul 2013, 19:48
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SravnaTestPrep wrote:
A and B together can complete one-ninth of a job in a day. What is the difference between the maximum and minimum number of days A could take to complete the job alone, if A and B take whole number of days to complete the job alone?
A 45
B.60
C.80
D.90
E.Cannot be determined

A and B together can complete one-ninth of a job in a day means that A & B together does one whole work in 9 days.
1/A +1/B = 1/9
The minimum value A can take is 10 days (Anything less than 10days is not possible because in other case, no of days taken by B will become negative, which is not possible practically)
When A takes least time (10Days) then B would take the Max time (90 days) to complete the work alone.

In order to find the Max time taken by A, find out the min time taken by B as we did earlier.
The minimum value B can take is 10 days (Anything less than 10days is not possible because in other case, no of days taken by A will become negative, which is not possible practically)
When B takes least time (10Days) then A would take the Max time (90 days) to complete the work alone.

So the required difference = Max Time taken-Min Time taken
= 90 - 10
=80 Days
Option C

Good conceptual question.
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Re: A and B together can complete one-ninth of a job in a day. [#permalink]  06 Aug 2013, 11:36
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Hello friends,

Is there any other way to do this question ?

Thanks & Regards
Vinni
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Kudos [?]: 1352 [3] , given: 219

Re: A and B together can complete one-ninth of a job in a day. [#permalink]  06 Aug 2013, 12:38
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vinnik wrote:
Hello friends,

Is there any other way to do this question ?

Thanks & Regards
Vinni

A pure algebraic way can be this:

$$rate*time=work$$

$$(A+B)*1=\frac{1}{9}$$ and $$A*t=$$1 and $$B*k=1$$ where t and k are the days A, B would take to finish the job and are integers.

From those we get: $$\frac{1}{t}+\frac{1}{k}=\frac{1}{9}$$ or $$t+k=\frac{tk}{9}$$. Lets study t (the time taken by A alone) $$t(1-\frac{k}{9})=-k$$ or $$t=\frac{-9k}{9-k}$$. How can we read this? Since k is a number the represents a number of days, must be positive=> -9k will be negative so because t must be positive, the denominator must be negative.
$$+ve=\frac{-ve}{-ve}$$.
$$9-k<0$$ so $$k>9$$, but since k is an integer => THE LEAST number of days B can take to finish the job is 10.

So if this is THE LEAST for B, it must be the MOST for A => $$t=\frac{-9*10}{9-10}=90$$.

You can repeat the whole analysis just by switching k and t and you find $$90-10=80$$.

Hope I've explained myself well (and hope you enjoy algebra )
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Re: A and B together can complete one-ninth of a job in a day. [#permalink]  07 Aug 2013, 03:20
Thanks Zarrolou

Regards
Vinni
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Kudos [?]: 168 [0], given: 102

Re: A and B together can complete one-ninth of a job in a day. [#permalink]  07 Aug 2013, 09:25
vinnik wrote:
Thanks Zarrolou

Regards
Vinni

solution:

1/A + 1/B = 1/9
when B max then A min. when B min A max. For minimum positive value(real), put B = 10 and consequently A=90. and vice versa. so difference= 90 - 10 = 80 (Answer)
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Re: A and B together can complete one-ninth of a job in a day. [#permalink]  26 Sep 2014, 07:24
1/A + 1/B = 1/9

so A = 9B/(B-9)

A will be max when denominator is minimum (1) so B = 10 and A = 90
For A to be minimum these values will just be reverse so A = 10
Difference 80
Re: A and B together can complete one-ninth of a job in a day.   [#permalink] 26 Sep 2014, 07:24
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