P, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour ?

Solution(By Examveda Team)

Let the number of pages typed in one hour by P, Q and R be x, y and z respectively
Then,
$$\eqalign{ & \Rightarrow x + y + z = \frac{{216}}{4} \cr & \Rightarrow x + y + z = 54z.....{\text{(i)}} \cr & {\text{ }}z - y = y - x \cr & \Rightarrow 2y = x + z.....{\text{(ii)}} \cr & {\text{ }}5z = 7x \cr & \Rightarrow x = \frac{5}{7}z......{\text{(iii)}} \cr} $$
Solving (i), (ii) and (iii), we get
$$\eqalign{ & x = 15, \cr & y = 18,{\text{ }} \cr & z = 21 \cr} $$