Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{Ravi}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} \cr & = \frac{{32}}{6} = \frac{{16}}{3} \cr & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{Kumar}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} \cr & = \frac{{40}}{5} = 8 \cr & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{both}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} \cr & = {\frac{{16}}{3} + 8} = \frac{{40}}{3} \cr & \therefore {\text{Time}}\,{\text{taken}}\,{\text{by}}\,{\text{both}}\,{\text{to}}\,{\text{type}}\,{\text{110}}\,{\text{pages}} \cr & = {110 \times \frac{3}{{40}}} {\text{hours}} \cr & = 8\frac{1}{4}\,{\text{hours}}\,{\text{(or)}}\,{\text{8}}\,{\text{hours}}\,{\text{15}}\,{\text{minutes}} \cr} $$