Multiple choice

$P$ can complete a work in $12$ days working $8$ hours a day. $Q$ can complete the same work in $8$ days working $10$ hours a day. If both $P$ and $Q$ work together, working $8$ hours a day, in how many days can they complete the work?

  1. $5\displaystyle\frac{5}{11}$
  2. $5\displaystyle\frac{6}{11}$
  3. $6\displaystyle\frac{5}{11}$
  4. $6\displaystyle\frac{6}{11}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P's total work time = 12 * 8 = 96 hours. Q's total work time = 8 * 10 = 80 hours. Rates: P = 1/96, Q = 1/80. Combined rate = (5+6)/480 = 11/480. Time for 8 hours/day = (480/11) / 8 = 60/11 = 5 and 5/11 days.

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