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Question 28 :Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

1. 40
2. 32
3. 36
4. 45

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Work and Time

Let a Human complete ‘H’ units of work per day and a Robot complete ‘R’ units of work per day
Given,
15H + 5R = \\frac{1}{30})^th work per day --- (1)
5H + 15R = \\frac{1}{60})^th work per day --- (2)
Dividing (1) and (2) by 5 and solving,
3H + R = \\frac{1}{150}) and H + 3R = \\frac{1}{300})

9H + 3R = \\frac{1}{50})
(-) H + 3R = \\frac{1}{300})
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8H = \\frac{1}{50}) - \\frac{1}{300}) => 8H = \\frac{1}{60})
H = \\frac{1}{480})
Work done by 15 Humans in a day = \\frac{15}{480}) = \\frac{1}{32})
No of days required for 15 humans to complete the work = 32 days

The question is "Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it? "

Hence, the answer is 32 days

Choice B is the correct answer.