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 they work on alternate days, let us consider a period of two days.
In a period of two days, work done by A and B
`=1//6+1//9=5//18`
If we consider 3 such time periods (we are considering 3 periods because in the fraction 5/18, the numerator 5 goes 3 times in the denominator 18),
Work done `=3xx(5//18)=15//18`
Remaining work `=3//18=1//16`
Now it is A's turn, since 3 whole numbers of periods are over.
Time taken by A to finish 1/16th of the work is one day.
So, total time taken `=(3xx2)+1=7` days.