A is thrice as efficient as B. A takes 24 days less than B to complete a work. If they work together, in how many days, will the work be completed?

9

Given,

A is thrice as efficient as B.

A : B = 3 : 1  (Efficiency)

Efficiency α \(\frac{1}{Time}\)

⇒ A : B = 1 : 3  (Time)

⇒ (3 -1)x = 24 days

⇒ 2x = 24 

⇒ x = 12 days,

⇒ Therefore, total work = 3 x 12 = 36 units,     ..(Efficiency × Days = Total work)

⇒ Time required by A + B to complete the work = \(\frac{36}{4}\) = 9 days,   ..(\(\frac{Work}{Efficiency}\) = Time)