Multiple choice

A and B can do a piece of work in 30 days and 45 days respectively. They start working together. After working three days A leaves and another person C joins to B. If B and C both finish the rest of work in 25/2 days then in how many days C can finish the work alone?

  1. 23⅔days

  2. 22½days

  3. 45 days

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A and B work for 3 days: 3 * (1/30 + 1/45) = 3 * (3/90 + 2/90) = 3 * 5/90 = 1/6. Remaining work = 5/6. B and C do 5/6 in 12.5 days, so their combined rate is (5/6) / 12.5 = 1/15. Since B's rate is 1/45, C's rate is 1/15 - 1/45 = 2/45. C takes 45/2 = 22.5 days.

AI explanation

Let the total work be the least common multiple of the given days, which is 90 units, making the daily work of A and B equal to 3 units and 2 units respectively. In the first 3 days, A and B together complete 5 units per day for 3 days, finishing 15 units and leaving 75 units of work. B and C finish the remaining 75 units in 12.5 days, meaning their combined daily work is 6 units; subtracting B's 2 units leaves C's daily work at 4 units. Therefore, C alone can finish the 90 units of work in 90 divided by 4 days, which equals 22.5 days.

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