Tim is thrice as good a workman as Joya and together they finish a piece of work in 75 days. In how many days will Tim alone finish the work?

100 days

According to the question,

Tim is thrice as good a workman as Joya, therefore,

⇒  Tim : Joya = 3 : 1  (Efficiency)

⇒ Tim + Joys complete a work in 75 days = (3 + 1) x 75 = 300 days,  ..(Efficiency × Days = Total work)

⇒ Time required by Tim alone to complete total work = \(\frac{300}{3}\) = 100 days,    ..(\(\frac{Work}{Efficiency}\) = Time)