A and B working separately can do a piece of work in 21 and 24 days, respectively. If they work for a day alternately with A beginning the work, it would be completed in _________.

$22\frac{3}{8}$ days

A = 21 days, B = 24 days,

⇒ They work on alternate days, starting with A,

 1st day = 8 units,

 2nd day = 7 units,

Every 2 days, 15 units of work is completed,

So in 22 days, 165 units of work is completed,

Therefore, in \( { 22}_{ 8}^{3 } \) days, total 168 units of work is completed.