Three typists P, Q and R, working together, can type 315 pages in 5 hours. In one hour, R types as many pages more than Q as Q types more than P. In 5 hours, R types as many pages as P types in 9 hours. How many pages can Q type in an hour?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 21
R is ahead of Q by the same number of pages as Q is ahead of P, so the three hourly rates are equally spaced and Q's rate is the average of the three.
Pages typed by all three in one hour \(\displaystyle =\frac{315}{5}=63\)
Write the rates as \(Q-d\), \(Q\), \(Q+d\); their sum is \(3Q=63\), so \(Q=21\)
The last condition fixes \(d\): \(5(21+d)=9(21-d)\), so \(14d=84\) and \(d=6\)
So P types 15, Q types 21 and R types 27 pages an hour, and \(5\times27=9\times15=135\)