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A can lay a railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in_________?

Correct answer: B. 9.6

  • A. 4
  • B. 9.6
  • C. 9
  • D. 10

Explanation

A's rate is 1/16 and B's rate is 1/12, so their combined rate is 7/48 work per day. Since A, B, and C together work at 1/4 = 12/48, C's rate is 12/48 - 7/48 = 5/48, giving C's time as 48/5 = 9.6 days. The likely mistake is 9 days, which comes from rounding the exact result incorrectly.

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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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