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

Question

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?

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

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

nick1816 · Accepted Answer

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

Archit3110 · Answer

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?

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

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

madgmat2019 · Answer

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

Posted from my mobile device

CareerGeek · Answer

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

eakabuah · Answer

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.

the answer is therefore D.

joohwangie · Answer

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

rate for 1 man working is 7n

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

1= /7n
1=210/7n
1= 30/n
n=30

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

Therefore, D

lacktutor · Answer

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.

The answer is D.

Posted from my mobile device

exc4libur · Answer

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

Answer (D)

PP777 · Answer

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

Correct answer=D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards