can do a piece of work in 8 hours and B can do the same work in 12 hours. In how much time both can finish the whole work working together?

A+B = (8×12)/(8+12)
=96/20
=24/5
=4. 4/5 days.
i.e, four four by five days.

efficiency varies inversely with time so A efficiency - 12 B efficiency -8 total work= 12*8 time taken by both= total work/ total efficiency of A and B time= 12*8/20 time = 4.8hrs

A's work in 1hr=1/8 ; B's work in 1hr=1/12

Total work in 1hr=1/8+1/12

                          =10/48 in 1hr

total time taken=48/10=4.8hrs