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John and Jack are assigned a certain job. On the first two days

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Suraj0184
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John and Jack are assigned a certain job. On the first two days [#permalink] New post   28 Jul 2022, 16:59
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53% (03:55) correct 47% (03:15) wrong based on 32 sessions
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John and Jack are assigned a certain job. On the first two days, they work together and complete 30% of the job by working 6 hours each day. In the next five days, John works alone for p hours each day and takes the job to 70% completion. On the next two days, Jack works for q hours each day and finishes the job completely. If p:q = 4:5, then find the value of p.

A. 8
B. 12
C. 16
D. 20
E. 24

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darshakvekaria
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Re: John and Jack are assigned a certain job. On the first two days [#permalink] New post   18 Aug 2022, 05:34
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John works alone for = 'p' hrs x 5 days = '5p' hrs
Work done = 0.4
Efficiency = 0.4/5p - (A)

Jack works alone for = 'q' hrs x 2 days = '2q' hrs
Work done = 0.3
Efficiency = 0.3/2q - (B)

We already know that p:q = 4:5 i.e., q=5p/4

In the first two days, efficiency of both the guys = 0.3/12hrs - (C)
Adding (A) and (B) to get (C)
0.4/5p + 0.3/2q = 0.3/12
Substituting q with it's equivalent in terms of p

0.4/5p + 0.3/(2*5p/4) = 0.3/12
p = 8
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Re: John and Jack are assigned a certain job. On the first two days [#permalink] New post   19 Aug 2022, 09:19
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they work for 2 days and completes .3 job

john- p hrs for 5 days to complete - (.7-.3) job = .4job
similarly
jack - q hrs for 2 days to complete (1-.7) = .3 job

so rate of John = work/time
.4job/5p
rate of jack = .3job/2q

since p/q = 4/5

.4/5p + .3/2q = .3/12 (in first two days both work for 12 hrs (6hrs a day ) and completed .3 of job )

solving we get p = 8
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Re: John and Jack are assigned a certain job. On the first two days [#permalink]
19 Aug 2022, 09:19
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