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A alone can finish a work in X days. B alone can finish the same work in X+5 days. Together, they take 6 days to complete the work. Find X

Correct answer: C. 10

  • A. 12
  • B. 8
  • C. 10
  • D. 9

Explanation

The combined rate equation is 1/X + 1/(X+5) = 1/6. Multiplying through gives 6(2X+5) = X(X+5), so X² - 7X - 30 = 0 = (X-10)(X+3), and the positive value is X = 10 days. The likely mistake is 8 days, which does not satisfy the combined-rate equation.

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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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