Multiple choice

A and B can complete a task in 36 days. However, A had to leave a few days before the task was completed and hence it took 54 days in all to complete the task. If A alone could complete the work in 48 days, how many days before the work getting over, did A leave?

  1. 25

  2. 30

  3. 24

  4. 28
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work rate is 1/48 per day. Combined rate is 1/36 per day, so B's rate is 1/36 - 1/48 = 1/144 per day. Let A leave x days before completion. Then (A+B) work together for (54-x) days at rate 1/36, and B works alone for x days at rate 1/144. Setting (54-x)/36 + x/144 = 1 gives 216 - 3x = 144, so x = 24 days.

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