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A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in___________days if they work together.

Correct answer: B. 22 ½ days

  • A. 18 days
  • B. 22 ½ days
  • C. 24 days
  • D. 26 days

Explanation

If B's rate is r jobs per day, A's rate is 3r jobs per day, so their times are 1/r days and 1/(3r) days. Their time difference is 1/r - 1/(3r) = 60 days, giving 2/(3r) = 60 days and r = 1/90 job per day. Together their rate is 4/90 job per day, so time = 90/4 days = 22.5 days. The likely mistake is option c, 24 days, from rounding or not applying the three-times rate correctly.

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About Time and Work

Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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