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# A can complete a project in 20 days and B can complete the

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Intern
Joined: 09 Sep 2012
Posts: 28
Location: United States
A can complete a project in 20 days and B can complete the  [#permalink]

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21 Sep 2012, 05:16
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00:00

Difficulty:

75% (hard)

Question Stats:

54% (01:37) correct 46% (02:04) wrong based on 576 sessions

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A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days
Math Expert
Joined: 02 Sep 2009
Posts: 49320
Re: A can complete a project in 20 days and B can complete the  [#permalink]

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21 Sep 2012, 05:35
12
3
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

The rate of A $$\frac{1}{20}$$ job per day;
The rate of B $$\frac{1}{30}$$ job per day.

Say they need $$t$$ days to complete the project.

According to the stem we have that B works for all $$t$$ days and A works only for $$t-10$$ days, thus $$\frac{1}{20}*(t-10)+\frac{1}{30}*t=1$$ --> $$t=18$$days.

Hope it's clear.
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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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21 Sep 2012, 05:49
2
3
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

Assume to total work to be 60 Units ( LCM of 20 & 30)
A does 3 units per day ( =60/20)
B does 2 units per day ( =60/30)
B works for 10 days alone work done = 2*10 = 20 units
A and B work together for the rest of the time
work left = 40 units
A and b together to 5 units oer day ( 2+3 = 5)
days required to do 40 units = 40/5 = 8

Total = 10+8 = 18
##### General Discussion
Intern
Joined: 09 Sep 2012
Posts: 28
Location: United States
Re: A can complete a project in 20 days and B can complete the  [#permalink]

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21 Sep 2012, 06:00
1
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.
Math Expert
Joined: 02 Sep 2009
Posts: 49320
Re: A can complete a project in 20 days and B can complete the  [#permalink]

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21 Sep 2012, 06:13
7
4
154238 wrote:
I am getting 27.. please tell me where i am going wrong.

The rate of A 1/20 job per day;
The rate of B 1/30 job per day:

If both are working together: 1/20 + 1/30 = 1/12, which means A and B working together will complete the project in 12 days.

if A left 10 days before the completion means they worked for 2 days together and B worked for 10 days more, so,
2*1/12 = 1/6 work done together => 5/6th project is remaining which wud be done by B,

B completes the project in.....30 days
B completes 5/6th project in......30*5/6=25

So, total of 25+2 = 27 days.

Please correct me if i am going in wrong direction.

Yes, working together they can complete the job in 12 days, but if A leaves at some point, then they no longer will need 12 days, they will need more. So, you cannot say that they worked together for 12-10=2 days.

Consider another approach:

In 10 days that B worked alone 10*1/30=1/3 of the job was done and 2/3 of the job was left to be done by A and B together.

Rate*Time=Job Done --> (1/20+1/30)*Time=2/3 --> Time=8. So, they worked together for 8 days, which means that total time is 10+8=18 days.

Hope it helps.
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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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21 Sep 2012, 10:26
A = w/20
B = w/30

A+B = w/20+w/30

Rate*Time = Work
(A+B)* (t-10) = W (A left the job 10 days before the total day)

solving we get t=28 days

putting total days = y-10= 28-10 = 18 days

I think I am wrong somewhere...
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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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14 Nov 2012, 07:08
1
1
d is the total days to complete the project.
A worked for d-10 days while b worked the whole d days.

Setup the Rate Equation like this $$(Rate of A) (d -10) + (Rate of B) (d) = 1$$

$$(\frac{1}{20}) (d-10) + (\frac{1}{30}) d = 1$$, 1 represents 100% of the project
$$3d -30 + 2d = 60 ==> 5d = 90 ==> d = 18 days$$

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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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11 Oct 2014, 12:12
I used logic and back solved to get this answer. We know the combined rate 12 days (1/30) + (1/20). So eliminate choice E as we know that A is stopping ten days earlier. Next look at 28 days and the 26.67 days. If we were to subtract 10 from each we would get something greater than 12 days, so we can eliminate those because if they worked together for more than 12 days the project would be complete. Next I looked at the 16 days subtracted out 10 days do this means they worked together for six days, completing half of the work (6 * (1/12)) and b would have 10 days (1/30) to complete the other half which is obviously not possible. Hence 18 is the answer
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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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24 Feb 2016, 11:19
A -> 1 day does 1/20 jobs
B -> 1 day does 1/30 jobs
=> (1/20+1/30)*t + 10*1/30=1 -> t=8 -> Time: 8+10=18 -> A
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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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05 Jun 2017, 19:11
1
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

1. (no.of days worked by A)/ (time normally taken by A working alone) + (no.of days worked by B)/ (time normally taken by B working alone) =1
2. Let B work on the project for x days which is also the time for completion of the project
3. (x-10)/20 +x/30 = 1, So x=18 days
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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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08 Jun 2017, 16:48
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

We are given that A can complete a project in 20 days and B can complete the same project in 30 days. Thus, the rate of A is 1/20 and the rate of B is 1/30. Since A quits 10 days before the project is completed, we can let t = the time in days worked by B, and thus, (t - 10) = the time in days worked by A. To determine t, we calculate the work done by A and the work done by B, using the work formula: work = rate x time.

work of A + work of B = 1

(1/20)(t - 10) + (1/30)(t) = 1

(t - 10)/20 + t/30 = 1

Multiplying the entire equation by 60, we have:

3t - 30 + 2t = 60

5t = 90

t = 18

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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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11 Sep 2017, 06:14
I did a very silly calculation mistake in this question-
(3+2)(x-10) + 2*10 = 60 should give us the number of days...
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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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20 Sep 2017, 11:51
Bunuel wrote:
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

The rate of A $$\frac{1}{20}$$ job per day;
The rate of B $$\frac{1}{30}$$ job per day.

Say they need $$t$$ days to complete the project.

According to the stem we have that B works for all $$t$$ days and A works only for $$t-10$$ days, thus $$\frac{1}{20}*(t-10)+\frac{1}{30}*t=1$$ --> $$t=18$$days.

Hope it's clear.

Hi Bunuel,

I understand the method but when I applied this on my own, I placed 1/T on the RHS of the equation instead of 1. Can you please help me understand why do we have 1 instead of 1/T on RHS?
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Joined: 02 Sep 2009
Posts: 49320
Re: A can complete a project in 20 days and B can complete the  [#permalink]

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20 Sep 2017, 11:58
TheMastermind wrote:
Bunuel wrote:
154238 wrote:
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

The rate of A $$\frac{1}{20}$$ job per day;
The rate of B $$\frac{1}{30}$$ job per day.

Say they need $$t$$ days to complete the project.

According to the stem we have that B works for all $$t$$ days and A works only for $$t-10$$ days, thus $$\frac{1}{20}*(t-10)+\frac{1}{30}*t=1$$ --> $$t=18$$days.

Hope it's clear.

Hi Bunuel,

I understand the method but when I applied this on my own, I placed 1/T on the RHS of the equation instead of 1. Can you please help me understand why do we have 1 instead of 1/T on RHS?

1/t is 1/(time), so rate.

The left hand side is (rate)(time) + (rate)(time) = (job done) + (job done) so it cannot equal to (rate), it should be the total (job done), which is 1.
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A can complete a project in 20 days and B can complete the  [#permalink]

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20 Sep 2017, 13:38
1
[quote="154238"]A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days

In 10 days B can do 1/3 of work

So A and B together have to do 2/3 of work

X(1/12) = 2/3
X= 8

So total 18 days.

Good question

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Re: A can complete a project in 20 days and B can complete the  [#permalink]

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27 Sep 2017, 18:32
A completes a project in 20 days which means A completes 5% of the project in a day.

B completes the same project in 30 days which means A completes 3.34% of the project in a day.

In a day, A&B together completes 8.34% of the project.

A quits 10 days before the project is completed, which means B completed 33.4% of the project on his own (10 days * 3.34% each day)

Therefore A&B together completed 66.6% of the project, so they must have worked for 8 days together. (66.6% / 8.34%)

So total time to finish the project = 10 + 8 = 18 days.
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Re: A can complete a project in 20 days and B can complete the &nbs [#permalink] 27 Sep 2017, 18:32
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