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# Bob and Alice can finish a job together in 3 hours.

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Intern
Joined: 08 Sep 2010
Posts: 48
Bob and Alice can finish a job together in 3 hours.  [#permalink]

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27 Oct 2011, 13:17
3
9
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:44) correct 23% (02:00) wrong based on 283 sessions

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Bob and Alice can finish a job together in 3 hours. If Bob can do the job by himself in 5 hours, what percent of the job does Alice do?
A) 10
B) 20
C) 40
D) 50
E) 60

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Re: Bob and Alice can finish a job together in 3 hours.  [#permalink]

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27 Oct 2011, 16:56
1
Lets supposat W is work Done and for moement we say that

W = 1 unit.

While working together --> W = Rate * Time = (1/A + 1/B)*3

...> 1 = 3 ( 1/A+1/B) --------- (1)

While only Bob is working , W = 1 = Rate of Bob & 5 .....> Rate of Bob = 1/B = 1/5 ---- (2)

Plugging 2 in (1) will give us Rate of Alice = 1/A = 2/15

Work Done by Alice = 2/15*3 = 2/5

% of workd done by Alice = 2/5*100 = 40% ---(C)
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Re: Bob and Alice can finish a job together in 3 hours.  [#permalink]

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28 Oct 2011, 00:50
1
2
You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 15 donuts which is the job ( I picked this as a SMART number).

Bob on his own works 15/5 = 3 donuts per hour.

Bob and Alice work 15/5 = 5 donuts per hour so Alice works 2 donuts/hour

To find out the percentage, Alice wroks 2 donuts/hr x 3 hours = 6 donuts per hour.

Therefore 6 donuts/15 donuts = 2/5 = 40%

hope this helped
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Re: Bob and Alice can finish a job together in 3 hours.  [#permalink]

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31 Jan 2016, 11:23
Hi All,

This prompt is a variation on a Work Formula question. It can actually be solved in a variety of ways - based on the information that we're given, here's a method that minimizes the number of calculations that you have to do:

We're told that Bob and Alice can finish a job together in 3 hours and that Bob can do the job by himself in 5 hours. We're asked what PERCENT of the job that Alice completes.

Since Bob can do the job in 5 hours, he completes 1/5 of the job per hour. We're told that he and Alice BOTH work for 3 hours, so Bob completes...

(3 hours)(1/5 of the job per hour) = 3/5 of the job = 60% of the job.

Since Bob completes 60% of the job, Alice must complete the other 40%.

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Re: Bob and Alice can finish a job together in 3 hours.  [#permalink]

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29 Mar 2017, 12:53
1
1/5 + 1/x = 1/3
1/x = 1/3 - 1/5
1/x = 2/5

2/5 x 100 = 40% Answer is C
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Re: Bob and Alice can finish a job together in 3 hours.  [#permalink]

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04 Apr 2017, 15:01
386390 wrote:
Bob and Alice can finish a job together in 3 hours. If Bob can do the job by himself in 5 hours, what percent of the job does Alice do?
A) 10
B) 20
C) 40
D) 50
E) 60

Since Bob and Alice can complete a job in 3 hours, the combined rate of Bob and Alice = 1/3. Since Bob can do the job by himself in 5 hours, his rate is 1/5.

Thus, the rate of Alice is 1/3 - 1/5 = 5/15 - 3/15 = 2/15.

Thus, when working together, the combined work is 1/3 and Alice's work is 2/15.

Since Alice has worked for 3 hours, her work is 3 x 2/15 = 2/5. Furthermore, since we consider the complete job the number 1, the percentage of the job done by Alice is:

(2/5)/1 = 2/5 = 40%

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Re: Bob and Alice can finish a job together in 3 hours.  [#permalink]

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15 Oct 2018, 07:58
Bob + Alice = 3 hours

Let's assume the total work as 30

Rate (Bob + Alice) = 30/3 = 10 units per hour

From the question, we know that Bob alone can finish the job in 5 hours. So let's find his rate of work.

Work = 30
Time = 5 hours
Rate = 30/5 = 6 units per hour.

Therefore in 3 hours, Bob alone can do 18 units and the remaining 12 will be carried out by Alice.

From the above information, we can find the rate of Alice.

Work = 12 units
Time = 3 hours
Rate = 12/3 = 4 units per hour

Now we need to find 12 is what percentage of 30
30x =1200
x =1200/30
x=40%

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Bob and Alice can finish a job together in 3 hours.  [#permalink]

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15 Oct 2018, 22:07
An easy approach:-

1/A+1/B=1/3

Given B=5

Solve and Get A=7.5

We are asked that what % of JOB does A do??

Time taken A:B= 7.5:5

Therefore :- Efficiency(work done) is inverse of time taken

Work done A:B= 5:7.5 =50:75=2:3

A does then (2/5) =40%
IMO C
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Joined: 08 Oct 2018
Posts: 3
Re: Bob and Alice can finish a job together in 3 hours.  [#permalink]

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16 Oct 2018, 10:04
1/3-1/5=2/15
(2/15)/(1/3)=2/5
2/5*100=40

ans: option c

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Re: Bob and Alice can finish a job together in 3 hours.   [#permalink] 16 Oct 2018, 10:04
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