If x persons take y days to complete z similar 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?

Let's say it takes 1 person 2 days to complete 4 jobs.
(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.

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

An alternate approach is to use the following equation:
(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.

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

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

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:

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