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?

Earnings are shared in the ratio of the work done by each person, which is proportional to their individual work rates or efficiencies.

1. From the first statement, "P works thrice as fast as Q", we can establish the ratio of P's work rate (Wp) to Q's work rate (Wq): Wp = 3 * Wq So, Wp : Wq = 3 : 1.

2. From the second statement, "P and Q together can work four times as fast as R": (Wp + Wq) = 4 * Wr (where Wr is R's work rate).

3. Now, let's combine these. Assume Q's work rate is 1 unit. If Wq = 1 unit, then Wp = 3 * 1 = 3 units. Substitute these into the second equation: (3 units + 1 unit) = 4 * Wr 4 units = 4 * Wr Wr = 1 unit.

4. Therefore, the ratio of their work rates is Wp : Wq : Wr = 3 : 1 : 1. Since earnings are shared in this ratio, they should share the earnings in the ratio 3:1:1.

Analyzing the options: A) 3:1:1 - This matches our calculated ratio. B) 3:2:4 - Incorrect, as Wq should be 1 when Wp is 3. C) 4:3:4 - Incorrect, as Wp:Wq is not 4:3. D) 3:1:4 - Incorrect, as Wr should be 1 when Wp is 3.

The final answer is A) 3:1:1.