Multiple choice

A task was assigned to P, Q and R to be completed in not more than seven days. P alone can complete the task in ten days. Q alone can complete the task in twelve days and R alone can complete the task in fifteen days. All three of them worked for two days and P and Q together worked for another two days. What portion of the task will remain after four days?

  1. 1/10

  2. 1/5

  3. 1/6

  4. 2/15

  5. 1/8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P's rate = 1/10, Q's = 1/12, R's = 1/15. Combined rate = (6+5+4)/60 = 15/60 = 1/4. Work in 2 days = 2 * 1/4 = 1/2. P+Q rate = 1/10 + 1/12 = 11/60. Work in 2 days = 2 * 11/60 = 11/30. Total work done = 1/2 + 11/30 = 15/30 + 11/30 = 26/30 = 13/15. Remaining = 1 - 13/15 = 2/15.

AI explanation

The daily work rates for P, Q, and R are 1/10, 1/12, and 1/15 respectively, summing to a combined rate of 1/4 per day. Working together for 2 days, they complete 2/4, or 1/2, of the task. The combined daily rate of P and Q is 1/10 plus 1/12, equaling 11/60, so their 2 days of work yield 22/60 of the task. The total work finished after 4 days is 1/2 plus 11/30, equaling 26/30, leaving a remaining portion of 4/30, which simplifies to 2/15.

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