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A certain tailor shop employs 10 workers who can normally complete an

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A certain tailor shop employs 10 workers who can normally complete an [#permalink]

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New post 29 Oct 2017, 20:42
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Question Stats:

49% (03:26) correct 51% (02:26) wrong based on 92 sessions

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A certain tailor shop employs 10 workers who can normally complete an ndustrial order in 112 days; however, the shop is prone to power outages, and each outages results in the loss of a full day of work. After 61 days working on a particular industrial order, the shop has had 5 power outages. At the beginning of the 62th day of work, in order to make up for the outages, the management hired 4 new workers who work at the same pace as the other employees. In the end, the order took 104 days to complete. How many power outages did the tailor shop have in total?

A. 2
B. 3
C. 5
D. 7
E. 8
[Reveal] Spoiler: OA

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Re: A certain tailor shop employs 10 workers who can normally complete an [#permalink]

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New post 29 Oct 2017, 20:57
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Lets say 1 worker can do 1 unit of work in 1 day. So 10 worker can do 10 units daily, and in 112 days they can do 10*112 = 1120 units. So here we are assuming that the total work to be done is equivalent to 1120 units (with 10 units happening daily as there are 10 workers).

Because of power outages, instead of 61 days, we've had only 56 days worth of work done, which is 56*10 = 560 units.
Remaining work = 1120-560 = 560 units.

To complete this remaining work, company has hired 4 more workers, so now work done daily would be = 10+4 = 14 units.
Going by this, days required to complete = 560/14 = 40 more.

But days actually taken to complete remaining work = 104-61 = 43. That means there have been 3 more power outages.

Total outages = 5 (earlier) + 3 = 8. Hence E answer

Kudos [?]: 183 [2], given: 284

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Re: A certain tailor shop employs 10 workers who can normally complete an [#permalink]

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New post 31 Oct 2017, 15:18
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anhht13 wrote:
A certain tailor shop employs 10 workers who can normally complete an ndustrial order in 112 days; however, the shop is prone to power outages, and each outages results in the loss of a full day of work. After 61 days working on a particular industrial order, the shop has had 5 power outages. At the beginning of the 62th day of work, in order to make up for the outages, the management hired 4 new workers who work at the same pace as the other employees. In the end, the order took 104 days to complete. How many power outages did the tailor shop have in total?

A. 2
B. 3
C. 5
D. 7
E. 8


The rate for the 10 workers is 1/112, so in the first 61 days, considering that they have had 5 power outrages, they complete 1/112 x 56 = 56/112 or 1/2 of the job.

Four new workers are hired, and they work at the same rate as the other workers. The original 10 workers worked at a rate of 1/112, and so the new crew of 14 individuals will work at a rate of n, which is calculated as follows:

10/(1/112) = 14/n

1120 = 14/n

1120n = 14

n = 14/1120 = 7/560 = 1/80

So, if there were no power outages, to complete the remaining half of the job, it would have taken (1/2)/(1/80) = 40 days, or a total of 101 days. However, since it took 104 day,s there must have been 3 additional power outages, bringing the total to 8 power outages.

Answer: E
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Re: A certain tailor shop employs 10 workers who can normally complete an [#permalink]

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New post 10 Nov 2017, 10:22
Even if you are completely bowled over by this question, you are chance of guessing the right answer is 33.33%
The question stem already tells us that there were 5 outages. Hence, the answer is at least 5. Given the tone of the question, if you were to guess, the answer would be more than 5, either D or E.
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A certain tailor shop employs 10 workers who can normally complete an [#permalink]

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New post 10 Nov 2017, 12:52
anhht13 wrote:
A certain tailor shop employs 10 workers who can normally complete an ndustrial order in 112 days; however, the shop is prone to power outages, and each outages results in the loss of a full day of work. After 61 days working on a particular industrial order, the shop has had 5 power outages. At the beginning of the 62th day of work, in order to make up for the outages, the management hired 4 new workers who work at the same pace as the other employees. In the end, the order took 104 days to complete. How many power outages did the tailor shop have in total?

A. 2
B. 3
C. 5
D. 7
E. 8


61 total days-5 outage days=56 work days
56 work days*10 workers*1/(10*112) daily rate per worker=1/2 order completed
104-61=43 total (work+outage) days remaining
let x=outage days remaining
(43-x) days*14 workers*1/(10*112) daily rate per worker=1/2 order remaining
x=3
3+5=8 total outages
E

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Re: A certain tailor shop employs 10 workers who can normally complete an [#permalink]

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New post 19 Nov 2017, 20:49
total work-day units = 112 X 10 = 1120
In 61 days , there is loss of 5 days . So actual work done = 56 X 10 = 560 work-day units.
Remaining work = 1120-560= 560 work-day units
From 62nd day total worker strength is 14. The work is completed in another 104-61 = 43 days.
therefore the total work-units by these 14 workers = 14 X 43 = 602 work -day units. Our requirement is 560, hence there must be additional power cuts during this period.
Difference = 602- 560 = 42 work-day units.
therefore no of days of additional power cut = 42/14 = 3 days
total : 5 days + 3 days = 8 days (must be the answer)

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Re: A certain tailor shop employs 10 workers who can normally complete an [#permalink]

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New post 04 Dec 2017, 21:20
A certain tailor shop employs 10 workers who can normally complete an ndustrial order in 112 days; however, the shop is prone to power outages, and each outages results in the loss of a full day of work. After 61 days working on a particular industrial order, the shop has had 5 power outages. At the beginning of the 62th day of work, in order to make up for the outages, the management hired 4 new workers who work at the same pace as the other employees. In the end, the order took 104 days to complete. How many power outages did the tailor shop have in total?

A. 2
B. 3
C. 5
D. 7
E. 8

===========
calculate total work:
total work done by 10 workers in 112 days = 10*112
Actual:
work done by 10 workers in 56 days (61-5(outage)) = 10*56

let number of outage days from 62nd day = x

no of days worked after 62nd day = 104-62+1 = 43

work done starting from 62nd day = 14 * (43-x)

10*112 = 10*56 + 14(43-x)

=> x =3

Total outage days = 3 + 5 = 8
Answer is E.

Kudos [?]: 0 [0], given: 3

Re: A certain tailor shop employs 10 workers who can normally complete an   [#permalink] 04 Dec 2017, 21:20
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