Harry can do a piece of work in 24 days. Peter can do the same work in 30 days and Vinod in 40 days. Harry and Vinod worked for 4 days and handed it to Peter. Peter worked for some days and handed it again to Harry and Vinod 6 days before completing the work. For how many days did Peter work?

Take total work as LCM(24,30,40) = 120 units. Harry does 5 units/day, Peter does 4 units/day, Vinod does 3 units/day. Harry and Vinod together do 8 units/day. They worked for 4 days initially and 6 days finally, totaling 10 days. Work done by H+V = 10 × 8 = 80 units. Remaining work = 120 - 80 = 40 units, done by Peter at 4 units/day, taking 40/4 = 10 days.