Raman can do a piece of work in 16 days. Satish can do the same work in 8 days while Ashok can do it in 32 days. All of them worked together when they started, but Satish left after 2 days. Raman left 3 days before the completion of work. How long did it take to complete the entire work?

Let us assume that the work to be done is 32 units i.e. the LCM of 8, 16 and 32.
Efficiencies of Raman, Satish and Ashok are 2, 4 and 1 units per day respectively.
Let us assume that they completed the work in X days.
Satish worked for 2 days, Raman worked for X-3 days and Ashok worked for X days which led to the completing of work in X days.
Total work done: 2*4 + (X-3)*2 + X*1 = 3X + 2.
This is equal to Total work = 32.
3X + 2 = 32
==> X = 10 days.