If 18 identical machines required 40 days to complete a job, how many

APPROACH #1: Machine days
18 identical machines required 40 days to complete a job
(18)(40) = 720
So it takes 720 "machine days" to complete the job

How many fewer days would have been required to do the job if 6 additional machines of the same type had been used from the beginning?
So we want to determine how many days it will take 24 machines to complete the job.
720/24 = 30 days complete the job with 24 machines

40 - 30 = 10
Answer: A

APPROACH #2: Assign a "nice" value to the job
Let's say the entire job consists of making 720 widgets (aside: This number works well with the given numbers of 18 and 40)
In other words, 18 machines can produce 720 widgets in 40 days
This means 18 machines can produce 18 widgets in ONE day (if we divide the time by 40, we also divide the output by 40)
This means ONE machine can produce 1 widget in 1 day (if we divide the number of machines by 18, we also divide the total output by 18)
This means 24 machines can produce 24 widgets in 1 day (if we multiply the number of machines by 24, we also multiply the total output by 24)
This means 24 machines can produce 720 widgets in 30 days (if we multiply the work time by 30, we also multiply the total output by 30)

40 - 30 = 10
Answer: A

Cheers,
Brent

Asked: If 18 identical machines required 40 days to complete a job, how many fewer days would have been required to do the job if 6 additional machines of the same type had been used from the beginning?

1 machine completes the job in 40×18 days
24= 18+6 machines will complete the job in = 40×18/24 = 30 days
Number of days saved = 40-30=10 days

IMO A

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The rate for the 18 machines is 1/40.

Let’s determine the rate of 24 machines using the following proportion:

18/(1/40) = 24/n

18n = 24/40

18n = 3/5

90n = 3

n = 3/90 = 1/30

So, the job is completed in 10 fewer days when 6 more machines are added.

Answer: A

1 machine completes the job in 40×18 days
24= 18+6 machines will complete the job in = 40×18/24 = 30 days
Number of days saved = 40-30=10 days

Alternate Method:
(Machine * Days) before = (Machine * Days) after
=> 18 * 40 = (18+6) * D
=> D=30 days when 6 machines are added.
Therefore, the difference is 40-30 = 10

Answer:A