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D01-28

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Joined: 02 Sep 2009
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16 Sep 2014, 00:12
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Difficulty:

55% (hard)

Question Stats:

67% (02:13) correct 33% (03:00) wrong based on 154 sessions

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Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of $$x$$?

A. $$1$$
B. $$1.25$$
C. $$2$$
D. $$2.5$$
E. $$4$$

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16 Sep 2014, 00:12
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Official Solution:

Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of $$x$$?

A. $$1$$
B. $$1.25$$
C. $$2$$
D. $$2.5$$
E. $$4$$

After 2 hours $$2*\frac{1}{10}=\frac{1}{5}$$ of the taks will be done (as only A works);

After 4 hours $$\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}$$ of the task will be done and $$\frac{1}{5}$$ will be left to be done;

We are told that 1/5th of the task is done in 15 minutes (1/4th of an hour) by all three workers: $$\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}$$. From which we can find that $$x=2$$ hours.

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31 Oct 2015, 21:04
1
A works alone for 2 hours,
0.2x(work) completed

joins B
0.2x completed by worker A
1/5 => 2/5 completed or 0.4x completed by worker B

after 4 hours we have 0.8x completed
joins C and everything is finished in 15 minutes
or 0.2x (work) is completed in 0.25 hours

now we can set an equation
1/10 + 1/5+ 1/x = 2/10 * 4/1 simplify 1/5 or 4/5
multiply everyting by 10
1+2+10/x = 8
10/x = 5
x = 2.
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22 Mar 2017, 08:35
not clear why 1/4 has been multiplied at end
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22 Mar 2017, 08:48
johncath wrote:
not clear why 1/4 has been multiplied at end

1 hour is 1.
15 minutes is 1/4
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04 Jul 2017, 06:01
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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04 Jul 2017, 06:05
Sangeeta2018 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

My friend, you should be more specific when asking a question. Which part is unclear? What to elaborate?
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25 Oct 2017, 04:53
The last calculation is not clear. How we are multiplying with with 1/4 and equalizing it to 1/5. I want to know the mathematical formula. Thanks
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25 Oct 2017, 05:10
1
Kamran23Z wrote:
The last calculation is not clear. How we are multiplying with with 1/4 and equalizing it to 1/5. I want to know the mathematical formula. Thanks

$$\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}$$.

(time)(combined rate) = (job done).
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25 Oct 2017, 22:50
Consider the total work as 10, and A can do 1 work in 1hr, B can do 2 work in 1 hr. A starts work for 2 hrs. So 2 work completed(1×2=2), then B joins for 2 hrs, so B does 4 work (2×2=4), now total work = A's 4+B's 4 work = 8. Balance work is 2. C joins and complete the work in 15 mins. That is A do .25 work and B do .5 work in15 mins., total .75 work(.25+.5=.75).Balace 1.25 work is done by C in 15 mins. So C can do 5 work in 1 hr. It means C takes 2hrs to complete the total work.
Ans : opt.c, 2hrs

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03 Nov 2017, 06:44
10 A = 5 B =Cx= k = since work remain same that each does

10A = since work remains the same

10 A = A*2 + (A+B)2 + (A+B+C) *1/4

=> K = K/10 *2 + (K/10+K/5)2 + (K/10 + K/5 +k/x) *1/4

solving for above equation

=> 1/2 = 1/x

x =2 hours for C
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30 Aug 2018, 22:15
A - 10 hours to complete the work
B- 5 hours to complete the work
C- X hours to complete the work
Take the LCM of 10,5,x = 10x (total work)
Hence A rate of work = 10x/10 = X units/hour
B rate of work = 10x/5 = 2x units/hour
C rate of work = 10x/x = 10 units/hour
therefore
X*2 +(2x+x)*2+(2x+x+10)*1/4 =10x
this gives X =2 (quick and easy)
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10 Sep 2018, 20:08
Hi Bunuel: Question M28-19 and D01-28 are the same. Just in case if it was not known earlier.
Re: D01-28 &nbs [#permalink] 10 Sep 2018, 20:08
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