Multiple choice

X and Y can complete a job separately in 40 and 60 days. After working together for 8 days, X leaves. What is the total time in which the work is completed?

  1. 48 days

  2. 44 days

  3. 46 days

  4. 40 days

  5. None of these
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A Correct answer
Explanation

X's rate = 1/40, Y's rate = 1/60. Together rate = 1/40 + 1/60 = 5/120 = 1/24. Work done in 8 days = 8/24 = 1/3. Remaining work = 2/3. Y completes 2/3 at rate 1/60, time = (2/3) * 60 = 40 days. Total time = 8 + 40 = 48 days.

AI explanation

Using the Least Common Multiple method, assume the total work is 120 units, making the daily work units of X and Y equal to 3 and 2 respectively. Working together for 8 days, they complete 8 * 5 = 40 units, leaving 80 units. Y completes these 80 units at 2 units per day, taking 40 days. The total time taken to complete the work is 8 + 40 = 48 days.

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