A can do a task alone in 96 days. B is thrice as efficient as A. A worked for 24 days alone and then B joined him. In how many days will they complete the remaining task together?

18

A = 96 days,

Given, 

B is thrice as efficient as A. therefore,

A : B = 1: 3   (Efficiency)

⇒ Total work = 1 x 96 = 96 units,   ..(Efficiency × Days = Total work)

⇒ A worked for 24 days alone = 1 x 24 = 24 units,

Remaining work = 96 - 24 = 72 units,

⇒ B joined A, so time required by them to complete the remaining work together = \(\frac{72}{1+3}\) = \(\frac{72}{4}\) = 18 days.    ..(\(\frac{Work}{Efficiency}\) = Time)