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. 36
• B. 32
• C. 45
• D. 40

Answer 1

The Correct Option is B

To solve this problem, we need to determine the number of days that fifteen humans will take to complete the job without robots. We are given:

• 15 humans and 5 robots take 30 days.
• 5 humans and 15 robots take 60 days.

Let's assume the work done by one human in one day is H and the work done by one robot in one day is R. The total work required to complete the job can be expressed in two equations based on the information given:

1. 15H + 5R = 1/30 

2. 5H + 15R = 1/60

We will solve these equations to find H and R. First, multiply the first equation by 2:

2(15H + 5R) = 2/30

30H + 10R = 1/15

Now, from the second equation:

5H + 15R = 1/60

Multiply by 2 to align the coefficient of H with the first (multiplied) equation:

10H + 30R = 1/30

Now subtract this equation from the first multiplied equation:

30H + 10R - 10H - 30R = 1/15 - 1/30

20H - 20R = 1/30

Solving for H and R, we get:

20H = 20R + 1/30

H = R + 1/600

Substitute H in one of the original equations, let's use the first one:

15(R + 1/600) + 5R = 1/30

15R + 15/600 + 5R = 1/30

20R + 1/40 = 1/30

Solving for R:

20R = 1/30 - 1/40

20R = 4/120 - 3/120

20R = 1/120

R = 1/2400

Now substitute R back to find H:

H = 1/2400 + 1/600

H = 1/2400 + 4/2400

H = 5/2400

H = 1/480

The work done by 15 humans in one day is:

15H = 15 × 1/480 = 1/32

Therefore, 15 humans will take 32 days to finish the job. The correct answer is 32.