A and B working separately can complete a piece of work in 10 and 16 days, respectively. If they work for a day alternately, with A beginning the work, in how many day(s) will the work be completed ?

$12\frac{1}{4}$

A = 10 days, B = 16 days

Since A and b are working on alternate days starting with A, 

1st day work (A) = 8

2nd day work (B) = 5    

      2 days work  = 13

So, in 12 days, 78 units of work will be completed 

The remaining work i.e; 2 units will be completed by A in \(\frac{2}{8}\) = \(\frac{1}{4}\) days.

Total time taken = \( { 12}_{4 }^{1 } \)