arithmetic
posted by Ramesh .
A and B can complete a piece of work in 8 and 10 days respectively However they work alternately one day each with beginning the work In how much time will the work be completed?

With WHO beginning the work? Person A? You seem to have left out a letter.
Assume A starts the job. After 1 day it will be 1/8 complete. After 8 days is will be 4/8 + 4/10 = 9/10 complete, and it will be A's turn again. The job will be completed near the end the ninth day.