Working alone, R can complete a certain kind of job in 9 hours. R and

working together R and S can complete the job in 6 hours
which means
1/R + 1/S =1/6
R can complete the job in 9 hours
therefore, 1/9+1/S=1/6
or,1/S=1/6-1/9
1/S=1/18
Thus S working alone can complete the job in 18 hours

Let total time taken by S to complete the job = S
total time taken by R to complete the job = 9
Work done by R in an hour
1/R = 1/9

Working together R and S can complete the job in 6 hours
1/R + 1/S = 1/6
=>1/S = 1/6 - 1/R
= 1/6 - 1/9
= 1/18
=> S = 18 hours

Answer A
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Hi All,

This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.

Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.

Here, we're told that R can complete a job in 9 hours and that R and S (when working together) can complete a job in 6 hours. We're asked how long it takes S to complete the job alone.

The 'twist' here is that we have to 'work back' to find the value of S...

(9)(S)/(9 + S) = 6

9S = 54 + 6S
3S = 54
S = 18 hours

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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if r and s be the amount of work done by R and S in 1 hour respectively.

then r=1/9 & r+s = 1/6 so s= 1/6-1/9 = 1/18

hence ans A

R alone : 9 hours

R and S together : 6 hours

S alone = ?

It can easily be seen that if S = 9, R and S = 4.5

Since R and S = 6, S is more than 9 i.e 12 or 18 from the answer choices

We know that time taken by R and S = \(\frac{(RS)}{(R+S)}\),

If we substitute R = 9, and S = 12 in the above formula, We get \(\frac{(9*12)}{(9+12)}\)

By inspection this is not an integer

So, We are left with S= 18

Choice A
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One approach is to assign a "nice" value to the entire job.
So let's use a number that works well with the two given values of 9 hours and 6 hours.
Let's say the job consists of making 54 widgets.

Working alone, R can complete a certain kind of job in 9 hours.
In other words, R can make 54 widgets in 9 hours.
This means R's RATE = 6 widgets per hour

R and S, working together at their respective rates, can complete one of these jobs in 6 hours
In other words, R and S can make 54 widgets in 6 hours.
This means their COMBINED rate = 9 widgets per hour

9 - 6 = 3
So, S's RATE = 3 widgets per hour

In how many hours can S, working alone, complete one of these jobs?
Another words, how much time will it take S to make 54 widgets?

Time = output/rate
So, time = 54/3 = 18 hours

Answer: A

Cheers,
Brent
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1/6- 1/9 = 1/18 ( rate)
Reciprocal is 18 ( hours)

The answer is A - 18, but how we come to this?

1/9 + 1/6 = 18

But how did we get 18 here?

It is
1/6-1/9 = 1/18

So S efficiency is 1/18 therefore will complete the job in 18 hrs

Posted from my mobile device

yeah, i got that it is 1/18

But 1/6 - 1/9 = 1/-3 ? no?
Where the number 18 appeared?

No it is not, that how you don't subtract it.
Take the lCM of denominator that is 18 then it goes in 6 three times and in 9 two times so 3-2 =1
Therefore subtracting value is 1/18

Where the number 18 appeared?[/quote]

No it is not, that how you don't subtract it.
Take the lCM of denominator that is 18 then it goes in 6 three times and in 9 two times so 3-2 =1
Therefore subtracting value is 1/18[/quote]

ah i see

thank you man!!!

We can create the equation:

1/S + 1/9 = 1/6

Multiplying by 18S, we have:

18 + 2S = 3S

18 = S

Answer: A

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Working alone R can complete the job in 1/9 hours
Working together R and S can complete the job in 6 hours i.e.
1/R + 1/S =1/6
Substituting 1/R
therefore, 1/9+1/S=1/6
or,1/S=1/6-1/9
1/S=1/18
Correct answer is A