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

Vaibhav efficiency = $$\dfrac {1}{60}$$

then according to question $$\dfrac{15}{60} + \dfrac{30}{S}  = 1  $$ (where S is sandeep work ) 

$$\Rightarrow \dfrac{30}{S} = 1 - \dfrac{1}{4}$$

$$\Rightarrow \dfrac {30}{S} = \dfrac {3}{4}$$

$$\Rightarrow S = \dfrac{3}{4}\times 30 $$

$$\Rightarrow S = 40 days $$ 

so sandeep finish work in 40 days when they work together then 

$$  \dfrac {1}{S} + \dfrac {1}{V} = \dfrac {1}{40} +\dfrac{1}{60}  $$ where V is vaibhav work

$$\Rightarrow \dfrac {6 + 4}{240} $$ 

$$\Rightarrow \dfrac {10}{240}$$ 

$$\Rightarrow \dfrac {1}{24}$$ (its efficiency both  V +S)

then vaibhav and sandeep work finish = 24 days Ans