A can do a piece of work alone in 12 days. B is 20% more efficient than A, and C is 25% more efficient than B. In how many days can B and C together complete the work?

$\frac{40}{9}$ days

A = 12 days,

    A  :  B  :  C 

    5  :  6

.   4  :      :  5

⇒ 10 : 12 : 15   (Efficiency)

⇒ Total work = A x 12 days = 10 x 12 = 120 units   ..(Efficiency × Days = Total work)

⇒ Time required by B + C to complete the total work = \(\frac{120}{27}\) = \(\frac{40}{9}\) days.      ..(\(\frac{Work}{Efficiency}\) = Time)