Multiple choice

A alone can do a piece of work in 14 days, which B alone can do in 21 days. They work together for 7 days, after which A quits. B is now joined by another person C, who does half as much work as A in a day. How many days will it take for B and C to complete the remaining work, after A quits?

  1. 4 days

  2. 3 days

  3. 2 days

  4. 1 day

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

A's rate = 1/14, B's rate = 1/21. Together = 1/14 + 1/21 = 3/42 + 2/42 = 5/42. In 7 days, they do 7 * 5/42 = 5/6 of the work. Remaining = 1/6. C's rate = 1/2 * A's rate = 1/28. B+C rate = 1/21 + 1/28 = 4/84 + 3/84 = 7/84 = 1/12. Time to finish 1/6 work = (1/6) / (1/12) = 2 days.

AI explanation

Assume the total work is the least common multiple of 14 and 21, which is 42 units. The daily work capacities are 3 units for A, 2 units for B, and 1.5 units for C, since C does half as much work as A in a day. Working together for 7 days, A and B complete 7 multiplied by their combined capacity of 5 units, finishing 35 units of work. The remaining 7 units are done by B and C, whose combined daily capacity is 3.5 units, so dividing 7 by 3.5 gives the result of 2 days.

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