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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?

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? Correct Answer 32

Calculation:

Let one human 1 day's work and one robot 1 day's work be 1/a and 1/b respectively.

⇒ 15/a + 5/b = 1/30

⇒ 5/a + 15/b = 1/60

Solving,

⇒ 1/a = 1/480

⇒ 15 humans 1 day' work = 15/480 = 1/32

∴ In 32 days, work will be completed by 15 humans.

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