Vaibhav can do a piece of work in 60 days. He works there for 15 days and then Sandeep alone finishes the remaining work in 30 days. In how many days will Vaibhav and Sandeep working together finish the work?

24 days

Vaibhav = 60 days,

Formula to be used here,

\( { M}_{1 } \) x \( { D}_{1 } \)  = \( { M}_{2 } \) x \( { D}_{2 } \)

where, M = No. of men, D = No. of Days,

⇒ Putting values in the formula,

⇒ Vaibhav x 45 = Sandeep x 30

⇒ 3 Vaibhav = 2 Sandeep

⇒ Vaibhav : Sandeep = 2 : 3 (Efficiency)

⇒ Total work = 2 x 60 = 120 units   ..(Efficiency × Days = Total work)

⇒ Time required for Vaibhav and Sandeep to complete the work together = \(\frac{120}{2+3}\) = \(\frac{120}{5}\) = 24 days.    ..(\(\frac{Work}{Efficiency}\) = Time)