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

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:

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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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