Humans and Robots Work Rates

CAT 2019 Slot 1 · QA · Easy · Work and Time

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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. A.

    40

  2. B.

    32

  3. C.

    36

  4. D.

    45

Answer

B

Explanation

Let daily rate of human = hh, robot = rr. Total work W=30(15h+5r)=450h+150rW = 30(15h + 5r) = 450h + 150r. Also W=60(5h+15r)=300h+900rW = 60(5h + 15r) = 300h + 900r. 450h+150r=300h+900r⇒150h=750r⇒h=5r450h + 150r = 300h + 900r \Rightarrow 150h = 750r \Rightarrow h = 5r. Total work W=450h+150(h/5)=450h+30h=480hW = 450h + 150(h/5) = 450h + 30h = 480h. Time taken by 15 humans alone = 480h15h=32\frac{480h}{15h} = 32 days.

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