Multiple choice

P and Q can do a work in 30 days and 18 days, respectively. P started the work and after 6 days, Q joined him to complete the work. In how much time was the total work done?

  1. 15 days

  2. 12 days

  3. 10 days

  4. 9 days

  5. None of the above
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A Correct answer
Explanation

P's rate = 1/30, Q's rate = 1/18. P works for 6 days alone: 6/30 = 1/5 work done. Remaining = 4/5. Combined rate = 1/30 + 1/18 = (3+5)/90 = 8/90 = 4/45. Time for remaining = (4/5) / (4/45) = 9 days. Total time = 6 + 9 = 15 days.

AI explanation

Assume the total work is the least common multiple of 30 and 18, which is 90 units. The daily work of P is 3 units and the daily work of Q is 5 units. P works alone for 6 days to complete 18 units, leaving 72 units of work. When P and Q join together, their combined daily capacity is 8 units, so they need 72 divided by 8, or 9 days, to finish the remaining work, making the total time 6 plus 9, which is 15 days.

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