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# One man started a project on the first day. One man joins on each day

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Math Expert
Joined: 02 Sep 2009
Posts: 59095
One man started a project on the first day. One man joins on each day  [#permalink]

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22 Oct 2019, 21:27
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Difficulty:

55% (hard)

Question Stats:

53% (02:14) correct 47% (02:23) wrong based on 34 sessions

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Competition Mode Question

One man started a project on the first day. One man joins on each day starting from the second day. The project will be completed in exactly 20 days. Instead, if a team of 7 men work regularly, the work will be completed exactly in n days. What is n?

A. 15
B. 20
C. 24
D. 30
E. 35

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Joined: 19 Oct 2018
Posts: 1077
Location: India
Re: One man started a project on the first day. One man joins on each day  [#permalink]

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22 Oct 2019, 22:01
2
Assume 1 man can do 1 unit of work everyday.

Total amount of work= 1+2+3......+20=$$\frac{20*21}{2}$$=210

A team of 7 men can perform work in a day= 7 units
Total number of days taken by team of 7 men = 210/7=30 days
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Re: One man started a project on the first day. One man joins on each day  [#permalink]

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22 Oct 2019, 23:14
1
work done ;
total men worked for 20 days ; 20*21/2 ; 210
210 =7*n
n=30 days
IMO D

One man started a project on the first day. One man joins on each day starting from the second day. The project will be completed in exactly 20 days. Instead, if a team of 7 men work regularly, the work will be completed exactly in n days. What is n?

A. 15
B. 20
C. 24
D. 30
E. 35
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Posts: 273
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: One man started a project on the first day. One man joins on each day  [#permalink]

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22 Oct 2019, 23:35
1
1st day = 1person
2nd day = 2persons
.
.
.
.
20th day = 20persons

So 1+2+3....20= 210persons work

If that work must be completed by 7 people it takes 210/7=30days

OA:D

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Re: One man started a project on the first day. One man joins on each day  [#permalink]

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23 Oct 2019, 00:08
1
Let the total work = 1 unit
Let the rate of work by each man = x units/day

So, Work done by man who worked for 20 days = 20x
Work done by man who worked for 19 days = 19x so on

--> Total work done for 20 days = 20x + 19x + 18x + . . . . . + 2x + x = 20/2*(20x + x) = 210x
--> 210x = 1
--> Rate of each man, x= 1/210

If 7 men work together, Rate = 7x = 7/210 = 1/30
--> Work = rate*time
--> 1 = 1/30*n = n/30
--> n = 30 days

IMO Option D
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Re: One man started a project on the first day. One man joins on each day  [#permalink]

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23 Oct 2019, 04:24
1
Given that it will take 20 days to complete a project with one man starting and a man joining the project each day from day 2, we are to find how many days it will take 7 people working together to complete the same piece of work.

Let x be the time it will take one person to complete the work.
From the information given in the question, we have an arithmetic progression with a common difference of 1, the last term is 20, and the first term is 1.
we need to find the sum and this sum will be x, the time taken for one person to complete the task.
x=20*21/2 = 210 days

Days taken for 7 people working together to complete the task, y, can be gotten as follows:
1/y=7/120
hence y=30 days.

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Joined: 17 Jan 2019
Posts: 127
Re: One man started a project on the first day. One man joins on each day  [#permalink]

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23 Oct 2019, 04:40
1
One man started a project on the first day. One man joins on each day starting from the second day. The project will be completed in exactly 20 days. Instead, if a team of 7 men work regularly, the work will be completed exactly in n days. What is n?

rate for 1 man working is 7n

1/(7n)+2/(7n)+3/(7n)...20/(7n)=1

1=[21(20)/2]/7n
1=210/7n
1= 30/n
n=30

A. 15
B. 20
C. 24
D. 30
E. 35

Therefore, D
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Posts: 343
Re: One man started a project on the first day. One man joins on each day  [#permalink]

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23 Oct 2019, 06:38
1
Let ‘a‘ be the work done by each person
1st day —$$a_{1}$$= 1a
2nd day—$$a_{2}$$= 2a
3rd day—$$a_{3}$$= 3a
.....
20th day—$$a_{20}$$= 20a
—> The amount of work done within 20 days —$$\frac{( 1a+20a)*20}{2}$$= 210a

If a group of seven people work together in this project, then
—> 7a*n= 210a
n = 30 days will take to complete the project.

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Joined: 24 Nov 2016
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One man started a project on the first day. One man joins on each day  [#permalink]

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Updated on: 24 Oct 2019, 04:53
Quote:
One man started a project on the first day. One man joins on each day starting from the second day. The project will be completed in exactly 20 days. Instead, if a team of 7 men work regularly, the work will be completed exactly in n days. What is n?

A. 15
B. 20
C. 24
D. 30
E. 35

rate•time=job
7(r)n=1
r=1/7n

day 1…20: (1 man * rate) + (2 man * rate) + (3 man * rate)…(20 man * rate) = 1 job
(1/7n)+(2/7n)…(20/7n)=1
1+2+…20=7n
210=7n
n=30

Originally posted by exc4libur on 23 Oct 2019, 08:33.
Last edited by exc4libur on 24 Oct 2019, 04:53, edited 1 time in total.
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Re: One man started a project on the first day. One man joins on each day  [#permalink]

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23 Oct 2019, 08:42
1
Let work done on 1st day = 1 unit
work done on 2nd day= 2 units
work done on 3rd day= 3 units
:
:
work done on 20th day= 20 units

Total work done in 20 days= 1+2+3+4+5+6+7+................+20
= 20(20+1)/2
=210......................................................(1)

Assuming amount of work done per day is same, so work done by 7 men in n days= 7n
From (1), we know that total work done is 210.
so, 7n=210
n= 30

Re: One man started a project on the first day. One man joins on each day   [#permalink] 23 Oct 2019, 08:42
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