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# T can work alone and will finish job in 6 hours, P & J can d

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T can work alone and will finish job in 6 hours, P & J can d [#permalink]  11 Aug 2011, 07:40
00:00

Difficulty:

45% (medium)

Question Stats:

48% (14:01) correct 52% (02:48) wrong based on 31 sessions
T can work alone and will finish job in 6 hours, P & J can do the same independently in 3 and 2 hours each. T starts working alone and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and they finish the job together. What was fraction of job done by T????

1) 1/9
2) 1/6
3) 1/3
4) 7/18
5) 4/9
[Reveal] Spoiler: OA

Last edited by KunalPratap on 11 Aug 2011, 20:26, edited 1 time in total.
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Re: Work time question [#permalink]  11 Aug 2011, 08:18
1
KUDOS
KunalPratap wrote:
T can work laone and finishes job in 6 hours, P & J can do the same independently in 3 and 2 hours each. P starts working and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and thet finish the job together. What was freaction of job done by P????

1) 1/9
2) 1/6
3) 1/3
4) 7/18
5) 4/9

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Re: Work time question [#permalink]  11 Aug 2011, 23:15
1
KUDOS
1st hour T works = 1/6 work completed = 1/6 remaining work = 5/6

2nd hour T works = 1/6 work completed = 1/6 + 1/3 = 1/2 remaining work = 5/6-1/2 = 1/3

when (1/6+1/3+1/2) all 3 work, it is completed in 1 hr

hence remaining work is completed in 1/3 hr

now in 60 min T completes 1/6 work
in 1/3 = 20 min T completes 1/9 work

thus, 1/6 + 1/6 + 1/9 = 4/9.

hence E.

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Re: Work time question [#permalink]  12 Aug 2011, 11:15
amit2k9 wrote:
1st hour T works = 1/6 work completed = 1/6 remaining work = 5/6

2nd hour T works = 1/6 work completed = 1/6 + 1/3 = 1/2 remaining work = 5/6-1/2 = 1/3

when (1/6+1/3+1/2) all 3 work, it is completed in 1 hr

hence remaining work is completed in 1/3 hr

now in 60 min T completes 1/6 work
in 1/3 = 20 min T completes 1/9 work

thus, 1/6 + 1/6 + 1/9 = 4/9.

hence E.

I did the same for the first two periods, but then in the third, 1/3 hr is left * T's 1/6th = 1/18, thus 7/18 total.

What am I misunderstanding?
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Re: Work time question [#permalink]  12 Aug 2011, 11:45
eragotte wrote:
amit2k9 wrote:
1st hour T works = 1/6 work completed = 1/6 remaining work = 5/6

2nd hour T works = 1/6 work completed = 1/6 + 1/3 = 1/2 remaining work = 5/6-1/2 = 1/3

when (1/6+1/3+1/2) all 3 work, it is completed in 1 hr

hence remaining work is completed in 1/3 hr

now in 60 min T completes 1/6 work
in 1/3 = 20 min T completes 1/9 work

thus, 1/6 + 1/6 + 1/9 = 4/9.

hence E.

I did the same for the first two periods, but then in the third, 1/3 hr is left * T's 1/6th = 1/18, thus 7/18 total.

What am I misunderstanding?

Same here. got D. Would be happy for an explanation if OA is E.

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Re: Work time question [#permalink]  13 Aug 2011, 16:02
First hour:

T: 1/6 job/hour * 1 hour = 1/6 job

Remaining work: 1 - 1/6 = 5/6 job

Second hour:

T: 1/6 job/hour * 1 hour = 1/6 job
P: 2/6 job/hour * 1 hour = 2/6 job

Remaining work: 5/6 - 3/6 = 2/6 job
T, P, J combined rate: 1 job/hour.
Remaining time to complete 2/6 job: 2/6 job / 1 job/hour = 2/6 hours

T: 1/6 job/hour * 2/6 hours = 2/36 = 1/18 jobs
P: 2/6 job/hour * 2/6 hours = 4/36 = 1/9 jobs
J: 3/6 job/hour * 2/6 hours = 6/36 = 1/6 jobs

Thus T completes 1/6 + 1/6 + 1/18 = (3 + 3 + 1)/18 = 7/18 of the job
P completes 2/6 + 1/9 = (6 + 2)/18 = 8/18 of the job
J completes 1/6 = 3/18 of the job

IMO:
[Reveal] Spoiler:
D
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Re: Work time question [#permalink]  14 Aug 2011, 00:57
I too got 7/18. If T works for 1 hr and complete 1/6 work then in 20 minutes (1/3 of an hour) T can finish 1/3 of job that T does in 1 hr. So it should be 1/6*1/3=1/18. So total work done by T is:
1/6+1/6+1/18=7/18.
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Re: Work time question [#permalink]  30 Oct 2011, 10:49
I got 7/18 toooo
could anyone plz explain why the answer is 4/9??
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Re: Work time question [#permalink]  31 Oct 2011, 22:01
1
KUDOS
Expert's post
KunalPratap wrote:
T can work alone and will finish job in 6 hours, P & J can do the same independently in 3 and 2 hours each. T starts working alone and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and they finish the job together. What was fraction of job done by T????

1) 1/9
2) 1/6
3) 1/3
4) 7/18
5) 4/9

T alone does the work in 6 hrs so rate = 1/6 work/hr
For P, the rate of work = 1/3 = 2/6 work/hr
For J, the rate of work = 1/2 = 3/6 work/hr
In first hour, T works alone so 1/6 of the work is done.
In the second hour, T and P work so 1/6 + 2/6 = 3/6 of the work is done. Now only 2/6 of the work is left.
In the third hour, they all work together at rate 1 work/hr (1/6+2/6+3/6)
Since only 2/6 of the work is left, time taken = 2/6 hr
Now, we know that T worked for the complete 2(2/6) hrs at the rate (1/6) so work done by T = (1/6)*2(2/6) = 7/18th of the entire work.

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Re: Work time question [#permalink]  02 Nov 2011, 07:36
Use respective work rates, I got:

(1)*1/6 + (1)*(1/6+2/6) + x*(1/6+2/6+3/6) = 1 (1 whole job)

Solving for x: 4/6 + x = 1 -> x = 2/6 = 1/3

So T worked for a total of 1+1+1/3 = 7/3 hours at the rate of 1/6 jobs per hour.

So T completed 7/3 * 1/6 = 7/18 of one job. Answer is D.
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Re: Work time question [#permalink]  13 Nov 2011, 13:01
I too also got D 7/18
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Re: Work time question [#permalink]  04 Jan 2012, 23:55
D should be the answer. E is wrong.
Re: Work time question   [#permalink] 04 Jan 2012, 23:55
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