CAT 2018 Slot 1 QA Question 7: 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 work

Question

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 work

Accepted Answer

Let the daily work done by one human and one robot be h and r respectively.
$15h + 5r = \dfrac{1}{30}$
$5h + 15r = \dfrac{1}{60}$
Multiply the first equation by 3 and subtract the second equation.
$45h + 15r = \dfrac{1}{10}$
$40h = \dfrac{1}{10} - \dfrac{1}{60} = \dfrac{1}{12}$
$h = \dfrac{1}{480}$