The ratio of time taken in completing a work by a man and woman is 2 : 3. The man and the woman can complete the work together in 24 days. In how many days can the woman complete the work alone ?

60 days

Efficiency ∝ \(\frac{1}{time}\)

                Man :  Woman 

Time           2   :    3

Efficiency    3   :     2  ⇒ total = 5

Total work = efficiency x no. of days 

                = 5 x 24 = 120

Time taken by woman alone = \(\frac{Total\; work}{efficiency}\)  

                                             = \(\frac{120}{2}\) = 60