Question

A alone can complete a work in 16 days B alone in 12 days. starting with A, they work on alternate days. the total work completed in how many days

Answer 1

let the work be completed in x days
A does 1/16 work in a day
B does  1/12 work in a day
So A has to work x/16 of work
     B has to work  x/12 of work
As they are working alternate day they would produce twice the work in x days
                           ⇒x/16+x/12=2
                           ⇒7x=96
                                 x=13.7=14
The work would be complete in 14 days.
                                                            

Answer 2

An easy way to do this problem is 
Let W be the work.
Then
A x 16 = W
B x !2 = W
 Total work to be completed is W
Since A and B are working in alternate days , only half of the work they do alone is required when they work together to complete the task.
Hence, 
A + B   = W
  2

16 + 12  = 28 = 14
     2          2

So the days taken to complete the whole work by A and B is 14 days.