If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
A. z
B. x
C. x/y
D. z/x
E. x/z
OA:E
How to use number plugging?
If x persons take y days to complete z similar jobs,
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Let's say it takes 1 person 2 days to complete 4 jobs.NandishSS wrote:If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
A. z
B. x
C. x/y
D. z/x
E. x/z
OA:E
How to use number plugging?
(so x = 1, y =2, and z = 4.)
If this person takes 2 days to do 4 jobs, it would take 2/4 or 1/2 a day to complete a single job.
If one person can do a job in 1/2 a day, 2 people (we said y = 2) would do the job twice as fast, so they'd only need 1/4 of a day.
So 1/4 is our target. Plugging in 1 for x and 4 for z, only E works.
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An alternate approach is to use the following equation:NandishSS wrote:If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
A. z
B. x
C. x/y
D. z/x
E. x/z
(workers)(time)/(output) = (workers)(time)/(output)
Since x people take y days to produce z jobs, and we want to determine the number of days for y people to produce 1 job, we get:
(x people)(y days)/(z jobs) = (y people)(t days)/(1 job)
xy/z = yt/1
x/z = t.
The correct answer is E.
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I think it's easiest to put it in words first.
Work = Rate * Time
z jobs = x people * (each person's rate) * y days
z/xy = each person's rate
From there, go to the equation we want:
1 job = y people * (each person's rate) * time
1 = y * z/xy * time
x/z = time
Work = Rate * Time
z jobs = x people * (each person's rate) * y days
z/xy = each person's rate
From there, go to the equation we want:
1 job = y people * (each person's rate) * time
1 = y * z/xy * time
x/z = time
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We are given that x people take y days to complete z similar jobs. Since rate = work/time, we can determine the rate of x people:NandishSS wrote:If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
A. z
B. x
C. x/y
D. z/x
E. x/z
rate of x people = z/y
To determine the rate for y people to complete 1 job, we can use a proportion to determine the rate of y people, in which n = the rate of y people. Our proportion read as:
"x people is to a rate of z/y as y people is to a rate of n"
x/(z/y) =y/n
xn = y(z/y)
xn = z
n = z/x
Since we have the rate of y people, we now can determine the time it takes for y people to complete 1 job.
time = work/rate
time = 1/(z/x) = x/z
Answer: E
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