Multiple choice

P, Q and R can complete a work in (a, b, c) days respectively where (a) is 20 less than (b), (c) is 50% more than (b). P starts the work and leaves after 12 days then Q completes the remaining work in 16 days. Find the time in which R can complete the work.

  1. 20

  2. 40

  3. 60

  4. 50

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given a=b-20, c=1.5b. Work equation: 12(1/a) + 16(1/b) = 1. Substituting a=b-20: 12/(b-20) + 16/b = 1. Solving: (12b + 16b - 320)/[b(b-20)] = 1, giving b² - 48b + 640 = 0, so (b-16)(b-40) = 0. b=40 (b≠16 since a would be negative). So c = 1.5×40 = 60 days. R alone takes 60 days.

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