Three typists P, Q and R, working together, can type 216 pages in 4 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 7 hours. How many pages can Q type in an hour?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 18
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 \(\displaystyle =\frac{216}{4}=54\)
Write the rates as \(Q-d\), \(Q\), \(Q+d\); their sum is \(3Q=54\), so \(Q=18\)
The last condition fixes \(d\): \(5(18+d)=7(18-d)\), so \(12d=36\) and \(d=3\)
So P types 15, Q types 18 and R types 21 pages an hour, and \(5\times21=7\times15=105\)