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?

CAT 2018 Question Paper | CAT Verbal Ability Slot 1

10 months ago

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?

A.
40
B.
32
C.
36
D.
45

Option B is the correct answer.

Explanatory Answer

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