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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 ?

a) 14, 17, 20
b) 15, 17, 22
c) 15, 18, 21
d) 16, 18, 22

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

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