Multiple choice

A and B can do a work in 10 days and 15 days respectively. If A starts on the work and both work alternatively day after day, in how many days will the work be completed.

  1. 9 days

  2. 10 days

  3. 11 days

  4. 12 days

  5. 14 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's daily work = 1/10, B's daily work = 1/15. In a 2-day cycle, they complete 1/10 + 1/15 = 5/30 = 1/6 of the work. In 10 days (5 cycles), they complete 5/6 of the work. On day 11, A does 1/10, total 5/6 + 1/10 = 16/15 (too much). A completes 1/6 of the remaining 1/6 on day 11, and B finishes the rest on day 12.

AI explanation

Taking the least common multiple of 10 and 15, the total work is 30 units, meaning A does 3 units per day and B does 2 units per day. Working on alternate days, their combined 2-day work is 5 units, so in 10 days they complete 25 units. On the 11th day, A does 3 units to finish the 28th unit, and on the 12th day, B completes the remaining 2 units, finishing the work in 12 days.

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