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A work is done by 15 workers not all of them have the same capacity to

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N22J
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A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   Updated on: 25 Jul 2020, 09:15
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A work is done by 15 workers not all of them have the same capacity to work. Every day exactly 2 workers do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for 5 more days to finish the work. Find the number of days in which all the workers together will finish the work?
A. 210
B. 105
C. 75
D. 20
E. 19
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E

Originally posted by N22J on 24 Jul 2020, 19:08.
Last edited by N22J on 25 Jul 2020, 09:15, edited 1 time in total.
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Re: A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   25 Jul 2020, 02:23
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Each worker has worked for 14 days in pair and for 5 additional days to finish the work. Hence, it will take 14+5=19 days to finish the work, if all the workers work together.



N22J wrote:
A work is done by 15 workers not all of them have the same capacity to work. Every day exactly 2 workers do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for 5 more days to finish the work. Find the number of days in which all the workers together will finish the work?
A. 210
B. 105
C. 75
D. 40
E. 20
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A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   25 Jul 2020, 04:14
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nick1816

This how I tackled this question

The work took 105 days when 2 pairs worked 15C2 + 5

Now when 15 people work, that is 7 times of 2 people approx; Thus we divide days by 7 as they are inversely proportional.
So we get 105/7 = 15+5 is this correct.
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Re: A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   25 Jul 2020, 08:14
If 15 workers comes in a pair till the time all possible pairs get exhausted then they have come for total 105 days and each day 2 workers have come so 210 workers has come. Now every worker comes has comes for equal number of days so
Each worker comes = 210÷15 = 14 days
After this all workers are working for 5 days together that means if they have to complete the work working together then they will take 19 days.

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Re: A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   25 Jul 2020, 09:04
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N22J wrote:
A work is done by 15 workers not all of them have the same capacity to work. Every day exactly 2 workers do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for 5 more days to finish the work. Find the number of days in which all the workers together will finish the work?
A. 210
B. 105
C. 75
D. 40
E. 20


Hi N22J. In the main question instead of "all the workers together take 5 more days" it should take 6 more days for all them working together to finish the work.
Then Option E would be correct.

If the statement that "all the workers together take 5 more days" is correct, then 19 days is the correct answer.

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Re: A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   25 Jul 2020, 09:17
Yes, u r right it has to be 19, I have changed the option..

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Re: A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   09 Aug 2022, 04:12
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"not all of them have the same capacity to work" in the question is confusing. If all of them do not have the same "capacity", it would mean we cannot assume the same rate of work for each worker, and then we can't solve the Ques.

Anyway, solving it by taking the same rate.

Let one worker's one day work be = x
For workers working in pairs, work for the day = 2x
Total days they work in pairs = 15C2
Total work done by workers working in Paris = 2x * 15C2
For the 5 days all workers work together, work done = 15x * 5

Total work done = 2x * 15C2 + 15x * 5
Don't calculate just yet.

Now, if all of them work together, work finished each day = 15x
Let total days = n
Total work = 15xn

Equate total work done (job to be completed is the same)
2x * 15C2 + 15x * 5 = 15xn
Calculate now, cancel 15.
14+5=n=19 days
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Re: A work is done by 15 workers not all of them have the same capacity to [#permalink] New post   09 Aug 2022, 04:54
Since each worker works with the other 14 workers once, the total number of days 1 worker will work in pairs will be 14.

Also, after the above 14 days of work, each worker will work again for the next 5 days with all the other workers.

Thus, the total number of days each worker worked = 19.

Let the efficiency of the 15 workers be a, b, c,.......o

Total work = 19(a+b+c+.....+o)

If all workers work together, total work done in a day = (a+b+c+.....+o)

Time taken by all the workers to finish the work = 19*(a+b+c+.....+o)/(a+b+c+.....+o) = 19

Thus, the correct option is E.
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Re: A work is done by 15 workers not all of them have the same capacity to [#permalink]
09 Aug 2022, 04:54
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