Multiple choice

$A$ can do a piece of work in $20$ days and $B$ in $40$ days. $A$ begins the work and there after they work alternately one on each day. On which day will the work be completed?

  1. $24$th day
  2. $25$th day
  3. $26$th day
  4. $27$th day
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A does 1/20 per day, B does 1/40 per day. In 2 days, they do 1/20 + 1/40 = 3/40. In 24 days (12 cycles), they do 12 * 3/40 = 36/40 = 9/10. On the 25th day, A does 1/20 (2/40), total 38/40. On the 26th day, B does 1/40, total 39/40. On the 27th day, A finishes the remaining 1/40.

AI explanation

The least common multiple of 20 and 40 is 40, which represents the total work units, meaning A does 2 units and B does 1 unit daily. Working alternately starting with A, they complete 3 units every two days, which means after 26 days they finish 39 units; A works on the 27th day to complete the final unit. The work is thus completed on the 27th day.

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