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by diebeatsthegmat » Tue Aug 23, 2011 7:06 pm
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
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by quantskillsgmat » Tue Aug 23, 2011 9:19 pm
i think answer shd be 7/12 which is nt in option.
total time for which t is working is 2 hrs 20 minues.
total time taken by all 3 is 4 hrs.
so fraction by t is 14/24=7/12
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by Anurag@Gurome » Tue Aug 23, 2011 9:29 pm
diebeatsthegmat 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????
In first 1 hour T finishes 1/6 of the work.
In next 1 hour T and P together finish (1/6 + 1/3) = 1/2 of the work.

Hence, remaining work = (1 - 1/2 - 1/6) = 1/3

In 1 hour three of them together finish (1/6 + 1/3 + 1/2) = 1, i.e. complete work.
To finish 1/3 of the work they will take 1/3 hours.

Hence, T has worked for (1 + 1 + 1/3) = 7/3 hours.
In this time T will finish (7/3)*(1/6) = 7/18 of the job.

The correct answer is D.
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by GMATGuruNY » Wed Aug 24, 2011 3:26 am
diebeatsthegmat 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
Let job = 6 units.
Rate for T = w/t = 6/6 = 1 unit per hour.
Rate for P = w/t = 6/3 = 2 units per hour.
Rate for J = w/t = 6/2 = 3 units per hour.

Work completed by T in 1 hour = r*t = 1*1 = 1 unit.

Combined rate for T and P = 1+2 = 3 units per hour.
Work completed by T+P in 1 hour = r*t = 3*1 = 3 units.

Remaining work = 6-1-3 = 2 units.
Combined rate for T,P and J = 1+2+3 = 6 units per hour.
Time to produce the remaining 2 units = w/r = 2/6 = 1/3 of an hour.

Total time for T = 1+1+(1/3) = 7/3 hours.
Work produced by T = r*t = 1*(7/3) = 7/3 units.
Fraction of work produced by T = (7/3)/6 = 7/18.

The correct answer is D.

If the OA is B, then the question must be asking for the fraction of the work produced by J.
Since J works only for 1/3 of an hour, work produced by J = r*t = 3*(1/3) = 1 unit.
Fraction of work produced by J = 1/6.
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by akhilsuhag » Wed Aug 24, 2011 3:42 am
diebeatsthegmat 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
Total Work: 6 (Assume)
S0 since T takes 6 hrs, his rate: 1/hr
P's Rate: 2/hr
J's Rate: 3/hr

Now T works for an hour, work done: 1
then P and T work for an hour, work done: 3 (1 + 2)

work left 2.

2= 6*t => t = 1/3.

How much work will T do in 1/3 hr.

w= 1*1/3 => 1/3

Total work done by T = 1+1+1/3 = 7/3.

Now (7/3)/6 = [spoiler]7/18 = D[/spoiler]

Basically calculate the amount of time T works and his rate.
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