Multiple choice

$A$ alone can complete a work in $16$ days and $B$ alone in $12$ days. Starting with $A$, they work on alternate days. The total work will be completed in.

  1. $12$ days
  2. $13$ days
  3. $13\dfrac{2}{7}$ days

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

A's rate is 1/16, B's is 1/12. In 2 days, they complete 1/16 + 1/12 = 7/48. In 12 days (6 cycles), they complete 6 * (7/48) = 42/48 = 7/8. Remaining work is 1/8. On day 13, A works and completes 1/16. Remaining is 1/8 - 1/16 = 1/16. On day 14, B completes it in (1/16) / (1/12) = 3/4 days. Total time = 13.75 days.

AI explanation

Let the total work be 48 units, so A does 3 units per day and B does 4 units per day. Working on alternate days starting with A, their combined output over a two-day cycle is 3 + 4 = 7 units. After 6 full cycles lasting 12 days, they complete 42 units, leaving 6 units unfinished. On the 13th day, A completes 3 units, leaving 3 units for B to complete on the 14th day, meaning the work is completed in exactly 14 days; since this is not listed, the result is none of these.

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