Multiple choice

$A$ and $B$ can complete a task in $12$ days. However, $A$ had to leave a few days before the task was complete and hence it took $16$ days in all to complete task. If $A$ alone could complete the work in $21$ days, how many days before the work getting over did $A$ leave?

  1. $7$
  2. $9$
  3. $5$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A's rate be 1/21. Let B's rate be x. Together (A+B) = 1/12. So 1/21 + x = 1/12, x = 1/12 - 1/21 = (7-4)/84 = 3/84 = 1/28. If the task took 16 days, and A worked for (16-y) days, then (16-y)/21 + 16/28 = 1. (16-y)/21 + 4/7 = 1. (16-y)/21 = 3/7 = 9/21. 16-y = 9, so y = 7.

AI explanation

The total work is the least common multiple of 12 and 21, which is 84 units, making the rates of A+B 7 units per day and A 4 units per day. Since B worked for all 16 days, B's rate is 7 minus 4, which is 3 units per day, yielding 48 units of work done by B. The remaining 36 units were done by A, which at 4 units per day takes A exactly 9 days of work. Therefore, out of the 16 total days, A left 7 days before the work was completed.

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