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N22J
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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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N22J
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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Yes, u r right it has to be 19, I have changed the option..

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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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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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