B is twice efficient as A and A can do a piece of work in 15 days. A started the work and after a few days B joined him. They completed the work in 11 days, from the starting. For how many days did they work together?

A can do a piece of work in 15 days.
B is twice as efficient as A.
So B can do the same piece of work in 7.5 days.
Assume the total work to be 15 units
A does 1 unit per day and B does 2 units per day.
For the first x days, A worked alone and hence work done per day is
1 * x = x units.
For the next (11 - x) days, A and B worked together. In 1 day, they will do (1 + 2) = 3 units.
So in 11 - x days, they will do 33 - 3x units.
33 - 3x + x = 15
2x = 18 and x = 9.
Thus A worked alone for 9 days the A and B worked together for 2 days.