Ram can do a work in 3 days, Shyam does 3 times the same work in 8 days and Rohit does 5 times the same work in 12 days. If they have to work together for 6 hours in a day, then in how much time can they complete the work?

5 hrs 20 min

Ram can do a work in 3 days, Shyam does 3 times the same work in 8 days and Rohit does 5 times the same work in 12 days.

Ram can do a work in = 3 days

Shyam can do a work in = \(\frac{8}{3}\) days

Rohit can do a work in = \(\frac{12}{5}\) days

So, Let total work = 24

Total efficiency of all together = 27

They all will finish the work in = \(\frac{24}{27}\) = \(\frac{8}{9}\) days

If they work only 6 hours in a day, then they all finish the work in = \(\frac{8}{9}\) × 6 hours = \(\frac{16}{3}\) = 5 hours 20 minutes