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 5/116 5/116 6/115 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 5/116 5/116 6/115 6/11
Solution
Sure, let's solve this step by step:
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First, we need to find out how many hours P and Q take to complete the work individually.
P can complete the work in 12 days working 8 hours a day, so P takes 12*8 = 96 hours to complete the work.
Q can complete the work in 8 days working 10 hours a day, so Q takes 8*10 = 80 hours to complete the work.
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Next, we need to find out how much work P and Q can do per hour.
P can do 1/96 of the work in one hour.
Q can do 1/80 of the work in one hour.
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If P and Q work together, they can do (1/96 + 1/80) of the work in one hour.
Adding these fractions together, we get (80 + 96) / (96*80) = 176/7680 = 1/44 of the work in one hour.
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If they work 8 hours a day, they can do 8/44 = 2/11 of the work in one day.
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Therefore, if they work together, they can complete the work in 1 / (2/11) = 11/2 = 5.5 days.
So, the answer is 5 1/2 days.
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