Pawan can do a piece of work in 32 days. He worked for 8 days and left the work. Thereafter Sandeep finished the remaining work in 27 days. In how many days can Pawan and Sandeep together do the whole work?

$16\frac{16}{17}$ days

Pawan = 32 days 

Let us assume his efficiency 1.

so the Total work = Efficiency x Time

          32 = 1 x 8

so he worked for 8 days, 

Efficiency x Time = Work

1 x 8 = 8,

Remaining work = 32 - 8 = 24

Sandeep completed remaining work in 27 days,

so his efficiency is = \(\frac{work}{time}\) = \(\frac{24}{27}\) =\(\frac{8}{9}\) 

Therefore time taken by both of them together to complete the whole work is,

   $\frac{32}{1+\frac{8}{9}}$   =  \(\frac{288}{17}\) 

  =\( {16 }_{17 }^{16 } \)days