Multiple choice

P and Q together can complete a work in 6 days. Q and R together can complete the same work in 15 days. P and R together can complete the work in 20/3 days. What is the ratio of number of days that Q alone takes to complete the work to the number of days that R alone takes to complete the work?

  1. 1:3

  2. 3:5

  3. 3:1

  4. 4:5

  5. 5:7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let rates be P+Q=1/6, Q+R=1/15, P+R=3/20. Adding these gives 2(P+Q+R) = 1/6 + 1/15 + 3/20 = (10+4+9)/60 = 23/60, so P+Q+R = 23/120. R = (P+Q+R) - (P+Q) = 23/120 - 20/120 = 3/120 = 1/40 (40 days). Q = (P+Q+R) - (P+R) = 23/120 - 18/120 = 5/120 = 1/24 (24 days). Ratio Q:R = 24:40 = 3:5.

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