15 Java programmers, working in a constant pace, finish a web page in

15 Java programmers, working in a constant pace, finish a web page in 3 days. If after one day, 9 programmers quit, how many more days are needed to finish the
remainder of the job
15 programmers finish a work in 3 days. So 1 programmer finished the same work in 3*15 = 45 days.
So 1 programmer contributed to 1/45 of the total work per day.

Now, we are told that 9 leave after day1. So total programmers left =6 => Total work contribution per day = 6*1/45 = 2/15
Work finished by now = 1/3. Left = 2/3.

Days required to complete work = (2/3) / (2/15) = 5. Hence the answer is A.

15 Java programmers can finish the job in 3 days = 15*3 = 45 programmer days
15 programmers in one day finish 1/3rd of the job , job left = 45-45/3=30 programmer days
programmers left after a day = 6
days required to complete the remaining job = 30/6 = 5 days

Assume total work is 45units
since 15 people complete work in 3 days so each worker works 1 unit each day

number of units completed on day 1 = 15*1 = 15
amount of work left = 45 - 15 = 30
Number of members that left = 9
Number of members remaining in the team = 15- 9= 6
Thus number of days needed to complete remaining work by remaining team = 30 /6 = 5

Ans :A

15 workers complete the work in 3 days.

That means 15 workers do (1/3)rd work in one day.

If after one day some 9 workers left, that means (1/3) work is done.

So (2/3)rd work has to be done.


Now 15 workers do (1/3)rd work in one day.

That means 1 worker does (1/45) work in 1 day
6 workers do (6/45) work in 1 day = (2/15) work in one day.

Days taken to compete 2/3 work:

(2/3) / (2/15) = 5 days.

A is the answer.

15 programmers -> 3 days
1 programmer ->45 days
Rate = 1/45

Day 1 : all 15 worked
therefore work done : RT = D
15* (1/45) * 1 = D

D = 1/3
1/3 of the work was done on day 1

Remaining days : 9 programmers quit , 6 remaining
work remaining = 1-1/3 = 2/3
Again, Rt = D
6* (1/45) t = 2/3
t = 5

hence (A)

Given:

3 day's work : x
1 day's work : x/3

Given:
15 people complete the work in 3 days .
After 1 day's work (x/3), 9 people left.
Remaining work = x - x/3 =2x/3

Now ,
1 day's work of 15 persons= x/3
1 day's work of 1 person = x/45.

1 day's work of 6 persons(15-9)= 2x/15.

2x/15 work completed in 1 day.
2x/3 work completed in = 5 days

Question asks how many more days needed to complete the remaining work,therefore 5 more days needed to complete the remaining work.

Answer is A.

One quick way to solve this:

15 build 1 site in 3 days = 1/3 of the site per day
After 9 leave, 6/15 or 2/5 of original number remain
rate of work per programmer remains constant so time required to do same amount of work per day increases by 5/2 (reciprocal of 2/5)
This means you need 5/2 days to build 1/3 of the site
2/3 of the site remains so you need (5/2)*2 days to build the rest

5 days needed

(2/3) / (2/15) is 10, right?
trying to follow, is it a typo?
thank you

As the question asked "how many more days?", shouldn't be answer 5-1=4 days?

Total job to be done = 15*3 = 45 units (1 unit of work is done by 1 worker in 1 day).

After one day, 1/3 of the job (15 units) is done and 30 units is left to be completed by 6 workers. 30 units will be done in 30/6 = 5 days.

Answer: A.

JeffTargetTestPrep The question asks how many more days, is this not 5 days - 3 days required = 2 days?

Hi Mco100,

I think the question asks how much more time the remaining programmers(after 9 leaving)
take in order to finish the work in hand(remaining 30 units).

If the question was asking how many more days, it would be 3, not 2 as the 15 programmers
would have already done one day's work.

Total job to be done = 15*3 = 45 units (assuming each worker does 1 unit of work in 1 day).

After one day, 15 units of the work is done. That same day 9 programmers leave.
There are a total of 6 programmers working to finish the 30 units, thereby completing
the remainder of the work in 5 days. So extra time taken will be \(1+5-3 = 3\)

Hope that helps you!

For one day there are 15 workers. They finish a fraction of the work. Some people leave. How many [more] days are needed for the new number of workers to finish the remaining work? You could take out the word "more."

That word, though, signals you to find the amount of work already done. It takes 5 days for 6 people to finish what is left. "Five days to finish" is five days more than one day.

Maybe trying individual rate will help. I think the work units and/or group efficiency methods might confuse. The group's numbers change, but the rate at which each person works does not. Fewer people to work equals more time to finish.

Find the rate of an individual programmer.

Just add (# of workers) to LHS in the standard (\(rt=W\)) formula. To find individual rate, you have to use t = 3 days

(# of workers * r * t) = W
# of workers = 15, \(r\) = ??, \(t = 3\), \(W = 1\)

\((15 * r * 3) = 1\)
\(45r = 1\)
\(r = \frac{1}{45}\)

At that individual programmer's rate, in ONE day, the amount of work that 15 workers will finish, (# * r * t) = W:

\((15 *\frac{1}{45} * 1) =(\frac{15}{45}) =(\frac{1}{3})\)
of work is finished.

\(\frac{2}{3}\) of work remains

But nine workers have gone. Use individual rate for the new number of workers.

How many [] days are needed for 6 workers to finish the remaining \(\frac{2}{3}\) of W?

(# of workers * r * t) = W
# of workers = 6, \(r =\frac{1}{45}\),\(t\) = ??, \(W =\frac{2}{3}\)

Time needed: \((6 *\frac{1}{45} * t)\) = \(\frac{2}{3}\)

\((\frac{6}{45}t) = \frac{2}{3}\)

\(t = (\frac{2}{3}) * (\frac{45}{6})\)

\(t\) = 5 days

Total days:
ONE DAY for 15 people to finish 1/3, and
FIVE DAYS for 6 people to finish 2/3

1 + 5 = 6 days' total.

After the first day (subtract it from the total days) it takes: (6 - 1) = 5 MORE days

Hope it helps!

one day work for one programmer = 1/45
one day work for 15 programmer = 15/45
remaining work = 30/45
remaining java programmer = 6
one day work of 6 java programmer = 6/45
so total days needed = 30/6 = 5 days

15 Java programmer complete a work in 3 days ..
1 Java programmer complete the work in 45 days..

Amount of work completed by 1 Java programmer in 1 day = 1/45

So, on 1st day amount of work completed = 1/45 * 15 = 1/3
Amount of work left at the end of the 1st day = 2/3
No. of programmers left after 1st day = 6

No. of extra days = (2/3)/(1/45* 6 ) = 5 days.

Answer A

We know that the daily rate of 15 workers is ⅓ of the job. To find the daily rate of 6 workers, then, we can set up the following proportion:

15/(1/3) = 6/x

45 = 6/x

45x = 6

x = 6/45 = 2/15 (This is the daily rate of 6 workers.)

Since after 1 day of work 1/3 of the job is completed, the 6 workers now have to complete the remaining 2/3 of the job at the rate of 2/15 of the job per day.

We use the formula work = rate x time. We let x = the time it will take the 6 workers to finish ⅔ of the job.

2/3 = (2/15)(x)

30/6 = x

x = 5

Answer: A

So - 15 programmers need 3 days
1 programmer needs 15 multiplied by 3 = 45 days
after 15 programmers worked for 1 day - they worked 15 days that are connected to 1 programmer
then 45-15 = 30 days left for one programmer
if 6 programmers are left
then 30/6 = 5 days
Answer A