CAT 2018 Quant Questions

Question:
Humans and robots can both perform a job but at di?erent e?ciencies. Fifteen humans and ?ve robots working together take thirty days to ?nish the job, whereas ?ve humans and ?fteen robots working together take sixty days to ?nish it. How many days will ?fteen humans working together (without any robot) take to ?nish it?

36
32
45
40
Show Answer
Correct Answer: 2

Let the efficiency of humans be 'h' and the efficiency of robots be 'r'.

In the first case, 

Total work = (15h + 5r) * 30......(i)

In the second case,

Total work = (5h + 15r) * 60......(ii)

On equating (i) and (ii), we get

(15h + 5r) * 30 = (5h + 15r) * 60

Or, 15h + 5r = 10h + 30r

Or, 5h = 25r

Or, h = 5r

Total work = (15h + 5r) * 30 = (15h + h) * 30 = 480h

Time taken by 15 humans = $\frac{\text{480h}}{\text{15h}}$ days= 32 days.

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CAT 2018 Quant Questions
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