Kajal can do a piece of work alone in 24 days, while Neha can do the same work alone in 40 days. Kajal started the work alone, and then after 12 days, Neha joined her till the completion of the work. How long did the work take to be completed since Kajal started to work on it ?

$\frac{39}{2}$ days

Kajal = 24 days, Neha = 40 days,

⇒ Kajal worked for 12 days alone = 5 x 12 = 60 units,   ..(Efficiency × Days = Work)

⇒ Remaining work = 120 - 60 = 60 units,

⇒ Neha joined Kajal and they completed the remaining work together = \(\frac{60}{5+3}\) = \(\frac{60}{8}\) = \( {7 }_{2 }^{1 } \) days,

⇒ Total time to complete the work since Kajal started working = 12 + \( {7 }_{2 }^{1 } \) = \(\frac{39}{2}\) days.