S does half as much work as T in 1/8 of the time taken by T. If they together complete a work in 60 days, then how many days shall S alone take to complete that work ?

75 days

S does half as much work as T in \(\frac{1}{8}\) of the time taken by T.

It means ratio of time :

                         S   :    T

Ratio of time =  1    :    8   (here S does half word as much as T)

Ratio of time =  2    :    8   (here S does as much work as T)

Ratio of Eff.   =  4    :    1   (Efficiency ∝ 1/time)

Now, ATQ,

S & T does the work together in 60 days.

Total work = Time × Effi. = 60 × (4 + 1) = 300

S alone does the work in = \(\frac{Total\;Work}{Effi.}\) = \(\frac{300}{4}\) = 75 days