# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Work and Time Questions | Question 28

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Question 28 :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. 40
2. 32
3. 36
4. 45

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##### Method of solving this CAT Question from Work and Time

Let a Human complete ‘H’ units of work per day and a Robot complete ‘R’ units of work per day
Given,
15H + 5R = $$frac{1}{30}$th work per day ---$1)
5H + 15R = $$frac{1}{60}$th work per day ---$2)
Dividing (1) and (2) by 5 and solving,
3H + R = $$frac{1}{150}$ and H + 3R = $\frac{1}{300}$ 9H + 3R = $\frac{1}{50}$$-) H + 3R = $$frac{1}{300}$ --------------------------- 8H = $\frac{1}{50}$ - $\frac{1}{300}$ => 8H = $\frac{1}{60}$ H = $\frac{1}{480}$ Work done by 15 Humans in a day = $\frac{15}{480}$ = $\frac{1}{32}$ No of days required for 15 humans to complete the work = 32 days The question is "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? "

##### Hence, the answer is 32 days

Choice B is the correct answer.

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