A can do a piece of work in 6 days working 8 hours a day while B can do the same work in 4 days working 10 hours a day. If the work has to be completed in 5 days, so how many hours do they need to work together in a day?

Working 8 hours a day, A can complete the work in 6 days i.e.

= $$8\times6=48$$ hours

Working 10 hours a day, B can complete the work in 4 days i.e.

= $$10\times4=40$$ hours

=> (A+B)'s 1 hour's work = $$\frac{1}{48}+\frac{1}{40}$$

= $$\frac{5+6}{240}=\frac{11}{240}$$

Thus, A and B can complete the work in $$\frac{240}{11}$$ hours

If they work for 5 days, number of hours required to complete the work = $$\frac{240}{11\times5}$$

= $$\frac{48}{11}=4\frac{4}{11}$$

=> Ans - (D)