P, Q and R three typist working simultaneously can type 456 pages in 6 hours. R can type as many pages in four hours as P in nine hours. In…

Let the number of pages typed in one hour by P, Q and R be x, y and z respectively

Then,

$ \Rightarrow x + y + z = \frac{{216}}{4} $

$ \Rightarrow x + y + z = 54z.....{\text{(i)}} $

$ {\text{ }}z - y = y - x $

$ \Rightarrow 2y = x + z.....{\text{(ii)}} $

$ {\text{ }}5z = 7x $

$ \Rightarrow x = \frac{5}{7} ........ $

Solving (i), (ii) and (iii), we get

$ x = 15, $

$ y = 18, $

$ z = 21 $