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# P,Q and R can do a piece of work in 4,6 and 12 days working

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Intern
Joined: 02 Jun 2013
Posts: 18
P,Q and R can do a piece of work in 4,6 and 12 days working  [#permalink]

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23 Oct 2013, 10:50
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Difficulty:

85% (hard)

Question Stats:

56% (03:43) correct 44% (03:41) wrong based on 78 sessions

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P,Q and R can do a piece of work in 4,6 and 12 days working 12 hrs a day.On each day p starts the work and works for 8 hrs then q works for 8 hrs and then r works for 8 hrs.in the same way they continue until p leaves after 2 days. then q and r work alternately for 8 hrs each till work is completed , in how many days is the work completed.

1) 10/3 days
2) 7/2 days
3) 11/3 days
4) 15/4 days
5) 21/4 days
Intern
Joined: 01 Aug 2013
Posts: 10
Location: United States
GMAT 1: 710 Q47 V41
GPA: 3.65
Re: P,Q and R can do a piece of work in 4,6 and 12 days working  [#permalink]

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23 Oct 2013, 12:03
1
I did this by adding each day up day-by-day

1. We have P doing the work in 4 (half) days, which means the work can be done in 2 full days, or 1/2 work/day
2. Q = 6(half) = 3 full = 1/3 work/day
3. R = 12(half) = 6 full = 1/6 work/day

So let's calculate the first day:

8 hours by P (1/3 of a day) = 1/3*1/2 = 1/6
8 hours by Q = ----------------- 1/3*1/3 = 1/9
8 hours by R ==-----------------1/3*1/6 = 1/18
Total per day with P,Q,and R is 6/18 = 1/3

The second day is the same, so after 2 days we have 2/3 completed.

The third day is just Q and R, so the first 8 hours will be Q (1/9), then R (1/18), then Q again (1/9)
Now that gives us 5/18, which when added to the first 2 days' total gives us 17/18 after 3 days

The fourth day starts with R, since Q finished day 3, and just needs to finish 1/18 of the total to complete the work, which we know takes R 8 hours.

Therefore, it takes 3 days 8 hours which can be confusingly written as 10/3 days.

Intern
Joined: 10 Jun 2019
Posts: 9
Re: P,Q and R can do a piece of work in 4,6 and 12 days working  [#permalink]

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21 Jun 2019, 17:59
2
1
P takes 4 days working 12 hrs/day to complete the job i.e. he takes 48 man-hours to complete the job.
Q takes 6 days working 12 hrs/day to complete the job i.e. he takes 72 man-hours to complete the job.
R takes 12 days working 12 hrs/day to complete the job i.e. he takes 144 man-hours to complete the job.

Taking the LCM of the total man-hours, let us say that the total work was 144 units.

If P completes 144 units in 48 hours, then P completes 24 units in 8 hours (by unitary method).
If Q completes 144 units in 72 hours, then Q completes 16 units in 8 hours (by unitary method).
If R completes 144 units in 144 hours, then R completes 8 units in 8 hours (by unitary method).

So on days 1 and 2, we have
First 8 hours (P) - 24 units
Next 8 hours (Q) - 16 units
Last 8 hours (R) - 8 units
Total - 48 units per day, so 96 units completed in 2 days.

Now, P leaves after day 2 while Q and R continue working alternatively. So on day 3, we have
First 8 hours (Q) - 16 units
Next 8 hours (R) - 8 units
Last 8 hours (Q) - 16 units
Total - 40 units per day

So, we have 136 units completed in 3 complete days and require 8 more hours to complete the task.

On day 4, resuming from who did the work last, we have
First 8 hours (R) - 8 units

So we have completed the task and taken 3 complete days and 8/24 => 1/3rd of the 4th day.

So total days taken => 3 + 1/3 = 10/3 days. Hence, Option A is the right choice.
Manager
Joined: 30 May 2019
Posts: 82
Re: P,Q and R can do a piece of work in 4,6 and 12 days working  [#permalink]

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01 Apr 2020, 22:08
sharankotagiri wrote:
P takes 4 days working 12 hrs/day to complete the job i.e. he takes 48 man-hours to complete the job.
Q takes 6 days working 12 hrs/day to complete the job i.e. he takes 72 man-hours to complete the job.
R takes 12 days working 12 hrs/day to complete the job i.e. he takes 144 man-hours to complete the job.

Taking the LCM of the total man-hours, let us say that the total work was 144 units.

If P completes 144 units in 48 hours, then P completes 24 units in 8 hours (by unitary method).
If Q completes 144 units in 72 hours, then Q completes 16 units in 8 hours (by unitary method).
If R completes 144 units in 144 hours, then R completes 8 units in 8 hours (by unitary method).

So on days 1 and 2, we have
First 8 hours (P) - 24 units
Next 8 hours (Q) - 16 units
Last 8 hours (R) - 8 units
Total - 48 units per day, so 96 units completed in 2 days.

Now, P leaves after day 2 while Q and R continue working alternatively. So on day 3, we have
First 8 hours (Q) - 16 units
Next 8 hours (R) - 8 units
Last 8 hours (Q) - 16 units
Total - 40 units per day

So, we have 136 units completed in 3 complete days and require 8 more hours to complete the task.

On day 4, resuming from who did the work last, we have
First 8 hours (R) - 8 units

So we have completed the task and taken 3 complete days and 8/24 => 1/3rd of the 4th day.

So total days taken => 3 + 1/3 = 10/3 days. Hence, Option A is the right choice.

Hello,

Could you please help me out here. The question says max number of working hours in any day is 12h, but you are taking all 24h. Why so?
Bunuel, could you please shed some light here?
Thank you
Intern
Joined: 09 Oct 2019
Posts: 6
Re: P,Q and R can do a piece of work in 4,6 and 12 days working  [#permalink]

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16 Apr 2020, 01:31
sharankotagiri wrote:
P takes 4 days working 12 hrs/day to complete the job i.e. he takes 48 man-hours to complete the job.
Q takes 6 days working 12 hrs/day to complete the job i.e. he takes 72 man-hours to complete the job.
R takes 12 days working 12 hrs/day to complete the job i.e. he takes 144 man-hours to complete the job.

Taking the LCM of the total man-hours, let us say that the total work was 144 units.

If P completes 144 units in 48 hours, then P completes 24 units in 8 hours (by unitary method).
If Q completes 144 units in 72 hours, then Q completes 16 units in 8 hours (by unitary method).
If R completes 144 units in 144 hours, then R completes 8 units in 8 hours (by unitary method).

So on days 1 and 2, we have
First 8 hours (P) - 24 units
Next 8 hours (Q) - 16 units
Last 8 hours (R) - 8 units
Total - 48 units per day, so 96 units completed in 2 days.

Now, P leaves after day 2 while Q and R continue working alternatively. So on day 3, we have
First 8 hours (Q) - 16 units
Next 8 hours (R) - 8 units
Last 8 hours (Q) - 16 units
Total - 40 units per day

So, we have 136 units completed in 3 complete days and require 8 more hours to complete the task.

On day 4, resuming from who did the work last, we have
First 8 hours (R) - 8 units

So we have completed the task and taken 3 complete days and 8/24 => 1/3rd of the 4th day.

So total days taken => 3 + 1/3 = 10/3 days. Hence, Option A is the right choice.

it's ok until the one highlighted
why 40 units per day for the sum of 24 hrs if the question says 12 hrs working a day ?

I got 2/3 : 5/18 * 2 = 2/3 * 18/5 * 2 = 24/5
Total days taken = 2 + 24/5 day

Intern
Joined: 26 Sep 2019
Posts: 8
Re: P,Q and R can do a piece of work in 4,6 and 12 days working  [#permalink]

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04 May 2020, 06:23
The question does not limit the daily working hour capabilities of machines, saying "working 12 hours a day". It mentions 12 hours only to give information about the capacities of machines. What it says if machine p would work 12 hours a day, it would complete the job in 4 days, alternatively it could say if machine p works 24 hours a day, it would complete the job in 2 days and nothing would change in the question.
Re: P,Q and R can do a piece of work in 4,6 and 12 days working   [#permalink] 04 May 2020, 06:23
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