Select the correct answerP 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 6/115 5/116 5/116 6/11
Question
Select the correct answerP 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 6/115 5/116 5/116 6/11
Solution
To solve this problem, we first need to find out how much work P and Q can do in an hour.
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P can complete the work in 12 days working 8 hours a day. So, the total hours P needs to complete the work is 12 days * 8 hours/day = 96 hours. Therefore, P's work rate is 1/96 of the work per hour.
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Q can complete the work in 8 days working 10 hours a day. So, the total hours Q needs to complete the work is 8 days * 10 hours/day = 80 hours. Therefore, Q's work rate is 1/80 of the work per hour.
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If P and Q work together, their combined work rate is 1/96 + 1/80 = 0.011458333 + 0.0125 = 0.023958333 of the work per hour.
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If they work 8 hours a day, they can do 0.023958333 * 8 = 0.191666664 of the work per day.
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Therefore, they can complete the work in 1/0.191666664 = 5.21 days.
So, the correct answer is 5 1/5 days, but this option is not given. There might be a mistake in the problem or the options provided.
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