P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P&Q and R together work on a job, in what ratio should they share the earnings?

Let’s take

Q’s work rate = 1 unit/day

P’s work rate = 3 units/day

So together, P + Q = 3 + 1 = 4 units/day

P and Q together work 4 times as fast as R

So R's work rate = (P + Q) / 4 = 4 / 4 = 1 unit/day


Now, we find total work rate of (P + Q) and R together:

(P + Q + R) = 4 (from above) + 1 = 5 units/day

So they should share the earnings in the ratio of their contributions:

P contributes: 3 units/day, Q contributes: 1 unit/day & R contributes: 1 unit/day
Therefore, the earnings should be divided in the ratio = P : Q : R = 3 : 1 : 1