A is 3 times as fast as B and is, therefore, able to complete a work in 32 days lesser than B. A and B, working together, can complete the work in _________.

12 days

Given,

A is 3 times as fast as B and is, therefore, able to complete a work in 32 days lesser than B.

                 A  :  B 

Time          1 :  3

Efficiency  3 :  1

⇒ 2T = 32 days,

⇒ T = 16 days,

⇒ Total work = 3 x 16 = 48 units,   ..(Efficiency × Days = Total work)

⇒ A + B can complete the work in = \(\frac{48}{(3+1)}\) = \(\frac{48}{(4)}\) = 12 days.       ..(\(\frac{Work}{Efficiency}\) = Time)