CAT 2018 Slot 1 QA Question & Solution
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?
Options
Solution
Let the efficiency of humans be $h$ and the efficiency of robots be $r$.
In the first case:
Total work = $(15h + 5r) \times 30 \quad \text{...(i)}$
In the second case:
Total work = $(5h + 15r) \times 60 \quad \text{...(ii)}$
By equating (i) and (ii), we get:
$$
(15h + 5r) \times 30 = (5h + 15r) \times 60
$$
Simplifying:
$$
15h + 5r = 10h + 30r
$$
$$
5h = 25r
$$
$$
h = 5r
$$
Now, the total work is:
$$
(15h + 5r) \times 30 = (15h + h) \times 30 = 480h
$$
The time taken by 15 humans to complete the work is:
$$
\frac{480h}{15h} \text{days} = \text{ 32 days}
$$
Hence, option C is the correct answer.