CAT 2018 Quant Questions

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 working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

36
32
45
40
Show Answer
Correct Answer: 2
Let the rates of work of each human and each robot be H and R respectively (both in units/day).
$15 \mathrm{H}+5 \mathrm{R}=\frac{1}{30}$ …… (1)
$5 \mathrm{H}+15 \mathrm{R}=\frac{1}{60}$ ……(2)
$3(1)-(2)=>40 \mathrm{H}=\frac{1}{12}$
$\mathrm{H}=\frac{1}{480}$
In a day, 15 humans can complete 15H i.e. $\frac{1}{32} t h$ of the job.
15 humans can complete the job in 32 days

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