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2 men and 12 women can finish a job in 4 days. 4 men and 6 women can do the same job in 5 days. Find the time taken by 1 man and 1 woman to complete the job.

Correct answer: C. 24 days

  • A. 30 days
  • B. 25 days
  • C. 24 days
  • D. 20 days

Explanation

Equalising the total work gives 4(2m + 12w) = 5(4m + 6w), so 8m + 48w = 20m + 30w and m = 3w/2. The job equals 4(2 × 3w/2 + 12w) = 60w units, while one man and one woman work at 3w/2 + w = 5w/2 units per day, so time = 60w ÷ 5w/2 = 24 days. The likely trap is 20 days, from failing to solve the man-to-woman efficiency ratio.

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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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