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A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

Correct answer: A. 37 ½ days

  • A. 37 ½ days
  • B. 22 days
  • C. 31 days
  • D. 22 days

Explanation

A completes 80% in 20 days, so A's rate is 0.8/20 = 0.04 = 1/25 work per day. Together they complete 20% in 3 days, giving a combined rate of 0.2/3 = 1/15, so B's rate is 1/15 - 1/25 = 2/75 and B alone needs 75/2 = 37.5 days. The likely mistake is 22 days, which does not follow from subtracting the two work rates 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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