This is a wonderful question from Work and Time that appeared in CAT 2018 Question Paper. This is a medium difficulty level question and one of those questions which boost your confidence in your CAT Exam. Picking a starting point to solve this question is crucial. Have a go at this question and watch the video explanation to see how Rajesh has solved it.
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?
Let a Human complete ‘H’ units of work per day and a Robot complete ‘R’ units of work per day
Given,
15H + 5R = 130th work per day --- (1)
5H + 15R = 160th work per day --- (2)
Dividing (1) and (2) by 5 and solving,
3H + R = 1150 and H + 3R = 1300
9H + 3R = 150
(-) H + 3R = 1300
---------------------------
8H = 150 - 1300 => 8H = 160
H = 1480
Work done by 15 Humans in a day = 15480 = 132
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? "
Choice B is the correct answer.
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