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If 3 men or 4 women can construct a wall in 43 days, then the number of days that 7 men and 5 women take to construct it is :

Correct answer: A. 12 days

  • A. 12 days
  • B. 14 days
  • C. 16 days
  • D. 18 days

Explanation

Since 3 men and 4 women do the same work in 43 days, 4 women have the work rate of 3 men, so one woman equals 3/4 of a man's rate. The rate of 7 men and 5 women is 7 + 5 x 3/4 = 43/4 man-units per day, while the work is 3 x 43 = 129 man-days; time = 129 / (43/4) = 12 days. The likely mistake is option b, 14 days, from treating a woman as equal to a man.

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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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