Multiple choice

$A$ and $B$ together can complete a work in 12 days. $A$ alone can complete it in 20 days. If $B$ does the work only for half a day daily, then in how many days will $A$ and $B$ together complete the work?

  1. $10$ days
  2. $11$ days
  3. $15$ days
  4. $20$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B = 1/12, A = 1/20. So B = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30. If B works half-time, his rate is 1/60. Combined rate = 1/20 + 1/60 = 4/60 = 1/15. Time taken = 15 days.

AI explanation

Using the standard work rate formula, B completes 1/12 minus 1/20 of the work per day, yielding 1/30. If B works for half a day daily, his effective daily contribution becomes half of 1/30, or 1/60. The combined daily work of A and the part-time B is 1/20 plus 1/60, totaling 4/60 or 1/15. Thus, they will complete the work together in 15 days.

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