Let us suppose, A and B can do a given work in 12 and 18 days respectively. They work alternately for equal period of time. And A started the work. Now, what is the time taken by A and B to complete the job?
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$A$ completes $\frac1{12}$ part of the work in $1$ day
$B$ completes $\frac1{18}$ part in $1$ day
So, in consecutive $2$ days, $A,B$ will complete $\displaystyle\frac1{12}+\frac1{18}=\frac5{36}$ part of the whole work
Now, $\left\lfloor \frac{36}5\right \rfloor=7$
So, in $2\cdot7=14$ days, they will complete $7\cdot\frac5{36}=\frac{35}{36}$ part of the whole work
The rest part of the work is $1-\frac{35}{36}=\frac1{36}$ and now it will be $A$'s turn first.
Now, $A$ does $\frac1{12}$ part in $1$ day
Can you take it from here?
lab bhattacharjee
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I am just a novice to the concept of arithmetic, I would be more than happy if you would help me with the full process. – Avery Dec 01 '13 at 14:18
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@user32340, we have $\frac1{36}$ part left and $14$ days consumed. Now, $A$ will complete the rest $\frac1{36}$ part in $\frac{12}{36}=\frac13$ day – lab bhattacharjee Dec 01 '13 at 14:20
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@user32340, please try to learn the relation among time,work & the resource? – lab bhattacharjee Dec 01 '13 at 14:31