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?

(a) 3 : 1 : 1 ✓ UPSC's answer
(b) 3 : 2 : 4
(c) 4 : 3 : 4
(d) 3 : 1 : 4

Why the answer is (a)

• Let the work rate of Q be 1 unit per day.

• Since P works thrice as fast as Q, P's rate is 3 units per day.

• The combined rate of P and Q is 3 + 1 = 4 units per day.

• The problem states that P and Q together work four times as fast as R, so 4 = 4 * (R's rate), which means R's rate is 1 unit per day.

• The ratio of their earnings is proportional to their work rates: P : Q : R = 3 : 1 : 1.

• Therefore, the correct option is (a).

Why the other options are wrong

(b) 3 : 2 : 4: Option (b) suggests Q works twice as fast as R, but both Q and R have a rate of 1 unit per day.
(c) 4 : 3 : 4: Option (c) incorrectly assigns a rate of 3 to Q and 4 to R, contradicting the derived rates of 1 and 1 respectively.
(d) 3 : 1 : 4: Option (d) incorrectly assigns a rate of 4 to R, whereas R's rate is 1 unit per day.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.