A and B can do a piece of work in 6 days and 9 days respectively, they work on alternative days starting with A on the first day. In how many days will the work be completed ?

Explanation

Since the work on alternate days, let us consider a period fo two days.
In a period of two days, work done by A and B =`(1)/(6)+(1)/(9)=(5)/(18)`
If we consider tree such time perods (we consider 3 periods because in the fraction `(5)/(18)`, the 5 goes three times in the denominator 18)
Remainin work `1-(15)/(18)=(3)/(18)=(1)/(6)`.
Now it is A's turn, since 3 whole number of period are over
Time taken by A to finish `(1)/(6)` of the work is one day
So, total time taken `=(3xx2)+1=7`