It takes 6 technicians a total of 10 hours to build and program a new

Great explanation by both!!

Kudos!!!

6 person can complete the job in 10 hours.
Rate of work per person per hour = x
W=R*T
1=6x*10
x=1/60

Work done by 6 persons for 6 hours at rate of (1/60)=
6*6*(1/60) = 6/10

Remaining Work = 1-6/10 = 4/10

4/10 = Y(1/60)

Y=24; at 5 pm no of persons were 7, at 6pm: 8, at 7pm :9persons, 7+8+9=24

Answer C

it took 3 hours after 5pm, to complete the task.

We should never, everrr make questions too complicated to infer and solve...
6 tech total of 10 hours... let me assume total of 60 units of work...
1 tech in 1 hr does 1 unit of work.....

11:00 am to 5:pm - 6 hours
so, total work done by 6 tech in 6 hrs will be 36 unit. ( 6*6)
now a new person gets added every hour after 5:00PM

11:00-5:00 - 36 unit
5:00-6:00 - 7 unit ( 6 tech were doing 6 unit in 1 hr, now since a new person has been added, the work increases to 7 unit)
6:00-7:00 - 8 unit ( another guy added)
7:00-8:00- 9 unit ( another guys added making total 9 person in the work field)

36+7+8+9 = 60.


so by 8:00PM 60 units of work was completed by the group....

Bingo..!!!!

1. Originally 6 people work for 60 man hours
2. Additional people work for 6 man hours
3. So to complete the same task since the same man hours is taken , the original 6 people work for 6 man hours less. i.e., they work for 60-6=54 man hours i.e., they work for 9 hours each
4 . In other words if they start the task at 11 A.M , they complete the task at 8:00 PM

The answer is choice C.

Makes me giggle how Bunuel always finds a simple yet understood solution! Though first I struggle to understand the problem and the previous posters' solutions!
Thanks Bunuel!

Man * Days * hours = Work done

6 people * 10 hours = 60 units

6 people * (11AM to 5 PM) 6 hours = 36

Work left 60-36 = 24

5-6 : 7 people = 7 units
6-7 : 8 people = 8 units
7-8: 9 people = 9 units
Total = 24 units

hence 8PM

So we need 60 hours men to finish the work
6 technitians will work for 6 hours hence they will do 36 hours. We now have 24 hours men left to complete
At 6pm - 7 hours men = 24 - 7 = 17
At 7pm - 8 hours men= 17-8 = 9
At 8pm- 9 hours men = Job Done

Hence answer is (C)

Hope it helps
Cheers!
J

Hi,
another method, though not easy and as simple as man-hours is--

in 6 hours, \(\frac{6}{10}\)work is completed...
left is \(\frac{4}{10}\)..
1 hour work of 6 is \(\frac{1}{10}\)...
and 1 hr work of 1 is\(\frac{1}{60}\)..
so from 5 pm onwards an AP can be formed..
\(\frac{1}{10} + \frac{1}{60} + \frac{1}{10}+\frac{2}{60} +\)...
let the hour required be x..
then\(\frac{1}{10}+\frac{1}{60} +\frac{1}{10} +\frac{2}{60}+.... \frac{1}{10} + \frac{x}{60}= 1-\frac{6}{10}\)
\(\frac{x}{10} + \frac{1}{60} ( 1+2+..+x) = \frac{4}{10}\)..
\(\frac{x}{10} + \frac{1}{60}*\frac{x(x+1)}{2}=\frac{4}{10}\)..
\(12x + x^2 + x = 48\)..
\(x^2 + 13x -48 =0\)..
\(x^2 + 16x - 3x -48 =0\)..
\((x+16)(x-3) =0\)..
so x=3 ..
time = \(5+3=8pm\)

We are given that 6 technicians can complete a job in 10 hours. Since rate = work/time, the rate of the 6 technicians is 1/10. Thus, the rate of 1 technician is (1/10)/6 = 1/60.

We see that 6 technicians work from 11:00 AM to 5:00 PM, or 6 hours. Since rate x time = work, those technicians complete 1/10 x 6 = 6/10 = 3/5 of the job.

If another technician is added to the job at 5:00 PM, the new rate for the technicians is (1/60) x 7 = 7/60, and thus all 7 technicians complete 7/60 of the job in the hour from 5:00 PM to 6:00 PM.

Thus, 3/5 + 7/60 = 36/60 + 7/60 = 43/60 of the job will be completed.

If another technician is added to the job at 6:00 PM, the new rate for the technicians is (1/60) x 8 = 8/60, and thus all 8 technicians complete 8/60 of the job in the hour from 6:00 PM to 7:00 PM.

Thus, 43/60 + 8/60 = 51/60 of the job will be completed.

If another technician is added to the job at 7:00 PM, the new rate for the technicians is (1/60) x 9 = 9/60, and thus all 9 technicians complete 9/60 of the job in the hour from 7:00 PM to 8:00 PM.

Thus, 51/60 + 9/60 = 60/60 = 1 whole job will be completed at 8:00 PM.

Answer: C

1. 1 technician will build in 60 hours or 60 man hours are needed
2. 6 technicians work for first 6 hours which is expending of 36 man hours
3. Similarly in the seventh, eighth , ninth hours, man hours expended are 7,8,9
4. Total man hours expended by the end of ninth hour is 36+7+8+9= 60 which will complete the job.
5. 11 A.M + 9 hrs is 8 PM

RT = W
6r10 = W
r =W /60

Technically Speaking, you require 60 man hours for the job which is the essence of the last equation.
Now From 11 AM to 5 PM . 6*6 = 36 manhours are already given.
So Remaining 60 - 36 = 24 hrs have to be done.

5-6 => 7 man hours
6-7 => 8 man hrs
7-8 => 9 man hrs

SO total = 7+8+9 = 24 hrs
Hence Answer = 8 PM.

Bunuel great explanation!!

Total work volume = 6 Tech * 10 Hours = 60 Units of work
6 Techs working together for 10 Hours complete 60 units of work
so each hour they complete 6 units of work
each tech completes 1 unit of work each hour

Based on this information, we see from 11am to 5pm, which is 6 hours, 36 units of work must be complete (6 hrs * 6 tech)
At 5pm 24 units of work is left to complete.

From 5pm to 6pm: 7 Tech are employed, so 7 units of work is completed, which makes it (36+7 = 43) units and 17 units is yet to complete
From 6pm to 7pm: 8 Tech are employed, so 8 units of work is completed, which makes it (43+8 = 51) units and 9 units is yet to complete
From 7pm to 8pm: 9 Tech are employed, so 9 units of work is completed, which makes it (51+9 = 60) units and they are done!

Hence, Option C (8:00pm)

It takes a total of 60 working hours to program the new server.
Since 6 technicians work for a period of 10 hours.
If starting at 11 : 00 am.
In the first six hours since 6 people are available: 36 hours of work done.
For the remaining 24 hours of work required.
After 5: 00 pm 7 hours of work done. ( 7 technicians )
From 6 to 7, 8 hours of work are done. ( 8  technicians )
From 7 to 8, 9 hours of work done : ( 9  technicians )
A total of 36 + 7+8+9 = 60 hours of work is finished at exactly 3 hours after 5: 00.
= 8 : 00 pm.

­Best way to do it. The other way takes nearly 3 minutes. This takes around 1.­


SVaidyaraman also explained it well! Thanks guys!