CAT 2018 Slot 1 — QA Question 10
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?
Answer & solution
- A
36
32
- C
45
- D
40
Let work-done by a human and a robot in a day are ‘h’ and ‘r’ respectively.
Work done by 15 human and 5 robot in 30 days = 30(15h + 5r)
Work done by 5 human and 15 robot in 60 days = 60(5h + 15r)
∴ Total work = 30(15h + 5r) = 60(5h + 15r)
⇒ 15h + 5r = 10h + 30r
⇒ h = 5r
Let fifteen humans take ‘y’ days to finish the job.
Work done by 15 humans in y days = y × 15
∴ 30(15h + 5r) = y × 15h
⇒ 30(15h + h) = y × 15h
⇒ y = 32
Hence, option (b).