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Q5 (CISF/2023) Miscellaneous & General Knowledge › Important Days, Places & Events

A, B and C alone can finish a job in 20, 25 and 30 days, respectively. A and B together start doing the job. However, they leave it after 10 days. The remaining part of the job is finished by C alone. How many days did C take to finish the job ?

Explanation

To solve this, we first determine the total work by calculating the Least Common Multiple (LCM) of the time taken by A, B, and C.

Total work = LCM(20, 25, 30) = 300 units.

  • Efficiency of A = 300 / 20 = 15 units/day
  • Efficiency of B = 300 / 25 = 12 units/day
  • Efficiency of C = 300 / 30 = 10 units/day

A and B work together for 10 days:

Combined efficiency of (A + B) = 15 + 12 = 27 units/day.
Work completed in 10 days = 27 × 10 = 270 units.

Remaining work = Total work - Completed work = 300 - 270 = 30 units.

Time taken by C to finish the remaining work = Remaining work / Efficiency of C = 30 / 10 = 3 days.

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SIMILAR QUESTIONS

CAPF · 2024 · Q40 Relevance score: 6.98

A, B and C can finish a work in 20, 25, and 30 days, respectively. They start working together but \(B\) quits after working for 3 days. In how many days from the start shall the work be completed?

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A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?

CAPF · 2022 · Q33 Relevance score: 5.90

Suppose A and B can complete a work together in 10 days. If B alone can complete the work in 15 days, then in how many days can A alone finish the work?

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Suppose, 'A' can complete a job in 10 days, and 'A' and 'B' together can complete the same job in 6 days. In how many days can 'B' alone complete the job ?

IAS · 2007 · Q55 Relevance score: 4.78

A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job?