Multiple choice

A can finish a work in 15 days, B can finish the same work in 25 days. They work together for 5 days. The rest of the work is finished by A and C in 4 days. Then C alone can finish the work in ?

  1. 18 days

  2. 24 days

  3. 20 days

  4. 21 days

  5. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/15, B's rate = 1/25. Combined = 8/75. In 5 days, they do 40/75 = 8/15. Remaining = 7/15. A and C do this in 4 days, so (1/15 + C) * 4 = 7/15 => 1/15 + C = 7/60 => C = 3/60 = 1/20. C takes 20 days.

AI explanation

Using the LCM method, let the total work be 75 units, so A's daily rate is 5 units and B's daily rate is 3 units. In 5 days, A and B together complete 8 times 5, or 40 units, leaving 35 units of work. A and C finish this remaining 35 units in 4 days, meaning their combined daily rate is 35 divided by 4, or 8.75 units. Subtracting A's rate of 5 from 8.75 leaves C with a daily rate of 3.75 units, so C alone requires 75 divided by 3.75, which equals 20 days to finish the work.

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