A and B together can finish a job in 40 days. A can do the same job on her own in 60 days. How long will B take to do the three-fourth of the same work all alone?

90 days

A + B = 40 days,

A = 60 days,

⇒ A + B = 3   (Efficiency)

⇒ 2 + B = 3

⇒ B = 1,

⇒ \(\frac{3}{4}\)th of total work = \(\frac{3}{4}\) x 120 = 90 units,

⇒ Time taken by B to complete 90 units of work = \(\frac{90}{1}\) = 90 days.  ..(\(\frac{Work}{Efficiency}\) = Time)