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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?Options5 5/115 6/116 5/116 6/11

Question

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?Options5 5/115 6/116 5/116 6/11

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Solution

Sure, let's solve this step by step:

  1. First, we need to find out how many hours P and Q take to complete the work individually.

    P takes 12 days * 8 hours/day = 96 hours to complete the work.

    Q takes 8 days * 10 hours/day = 80 hours to complete the work.

  2. Next, we find out how much work P and Q can do in an hour.

    P can do 1/96 of the work in an hour.

    Q can do 1/80 of the work in an hour.

  3. If they work together, in an hour they can do 1/96 + 1/80 of the work.

    This equals to (80 + 96) / (96 * 80) = 176/7680 = 1/44 of the work in an hour.

  4. If they work 8 hours a day, in a day they can do 8/44 = 2/11 of the work.

  5. Therefore, to complete the whole work, they will need 1 / (2/11) = 11/2 = 5.5 days.

So, the answer is 5 1/2 days.

This problem has been solved

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