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X takes 10 days to complete a task. Y takes half that time [#permalink]
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Updated on: 17 Jun 2014, 05:32
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X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together? A. 2 B. 3 C. 4 D. 5 E. 6
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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17 Jun 2014, 05:23
X takes 10 days to complete the work > X completes 1/10th of the work in 1 day Y takes 5 days to complete the work > Y completes 1/5 i.e 2/10th of the work in 1 day.
together X and Y can complete 1/10 + 2/10 = 3/10 , of the work in 1 day > X and Y take 10/3 days to complete the work together.
the problem says, X already completed 40% of the work, i.e X and Y together completed the remaining 60%
time taken to complete that is 10/3 * 60/100 = 2 days.
answer option A, 2 days



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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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17 Jun 2014, 05:33
I have edited the question to remove any ambiguity.
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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17 Jun 2014, 07:30
SravnaTestPrep wrote: I have edited the question to remove any ambiguity. Alone X takes 10 days to complete the task. Therefore rate of x=1/10 Y takes half the time to complete the task. Therefore Y's rate is double of X's rate=1/5 Let x be the total number of days A worked. Work=Rate*Days 40/100=1/10*x x=4 Let y be the total number of days B worked. Work=Rate*Days 60/100=1/5*y y=3 A worked for total 4 days and B worked for total 3 days. Hence both worked together for 3 days. Ans=B



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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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17 Jun 2014, 09:01
SravnaTestPrep wrote: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2 B. 3 C. 4 D. 5 E. 6 let the work be 100 units. since X takes 10 days to complete a task therefore x will do(100/10) 10 units per day and thus y will do 20 units per day. therefore x and y 's combined 1 day work will be 10+20=30 units now since y has completed 60% of the work by working with X, therefore x and y must have worked for 3 days. hence answer should be B



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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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18 Jun 2014, 02:29
Work rate of \(X = \frac{1}{10}\) Work rate of Y\(= \frac{1}{5}\) Combined rate \((X & Y) = \frac{1}{10} + \frac{1}{5} = \frac{3}{10}\) Say X works alone for "a" days & (X + Y) work for "b" days Work Done only by \(X = \frac{1}{10} . a\) Total Work Done \(= \frac{1}{10} . a + \frac{3}{10} . b\) \(= \frac{a + 3b}{10}\) 40% of Total work done = Work done by X \(\frac{40}{100} \frac{(a + 3b)}{10} = \frac{a}{10}\) a = 2b I end up here.... Bunuel, can you kindly suggest next step........... or is the complete approach wrong?
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X takes 10 days to complete a task. Y takes half that time [#permalink]
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19 Jun 2014, 02:07
PareshGmat wrote: Work rate of \(X = \frac{1}{10}\)
Work rate of Y\(= \frac{1}{5}\)
Combined rate \((X & Y) = \frac{1}{10} + \frac{1}{5} = \frac{3}{10}\)
Say X works alone for "a" days & (X + Y) work for "b" days
Work Done only by \(X = \frac{1}{10} . a\)
Total Work Done \(= \frac{1}{10} . a + \frac{3}{10} . b\)
\(= \frac{a + 3b}{10}\)
40% of Total work done = Work done by X
\(\frac{40}{100} \frac{(a + 3b)}{10} = \frac{a}{10}\)
a = 2b
I end up here....
Bunuel, can you kindly suggest next step........... or is the complete approach wrong? Let me try to answer. The mistake is, Work done by x = (a + b)/10 You will then get b=3a. Substituting in the equations you will get b=3 which is the total number of days X and Y worked together.
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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19 Jun 2014, 05:10
SravnaTestPrep wrote: PareshGmat wrote: Work rate of \(X = \frac{1}{10}\)
Work rate of Y\(= \frac{1}{5}\)
Combined rate \((X & Y) = \frac{1}{10} + \frac{1}{5} = \frac{3}{10}\)
Say X works alone for "a" days & (X + Y) work for "b" days
Work Done only by \(X = \frac{1}{10} . a\)
Total Work Done \(= \frac{1}{10} . a + \frac{3}{10} . b\)
\(= \frac{a + 3b}{10}\)
40% of Total work done = Work done by X
\(\frac{40}{100} \frac{(a + 3b)}{10} = \frac{a}{10}\)
a = 2b
I end up here....
Bunuel, can you kindly suggest next step........... or is the complete approach wrong? Let me try to answer. The mistake is, Work done by x = (a + b)/10 You will then get b=3a. Substituting in the equations you will get b=3 which is the total number of days X and Y worked together. I tried it; however not getting through Equation comes up a follows: \(\frac{40}{100} . \frac{a+4b}{10} = \frac{a+b}{10}\) a = b
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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19 Jun 2014, 07:45
PareshGmat wrote: SravnaTestPrep wrote: PareshGmat wrote: Work rate of \(X = \frac{1}{10}\)
Work rate of Y\(= \frac{1}{5}\)
Combined rate \((X & Y) = \frac{1}{10} + \frac{1}{5} = \frac{3}{10}\)
Say X works alone for "a" days & (X + Y) work for "b" days
Work Done only by \(X = \frac{1}{10} . a\)
Total Work Done \(= \frac{1}{10} . a + \frac{3}{10} . b\)
\(= \frac{a + 3b}{10}\)
40% of Total work done = Work done by X
\(\frac{40}{100} \frac{(a + 3b)}{10} = \frac{a}{10}\)
a = 2b
I end up here....
Bunuel, can you kindly suggest next step........... or is the complete approach wrong? Let me try to answer. The mistake is, Work done by x = (a + b)/10 You will then get b=3a. Substituting in the equations you will get b=3 which is the total number of days X and Y worked together. I tried it; however not getting through Equation comes up a follows: \(\frac{40}{100} . \frac{a+4b}{10} = \frac{a+b}{10}\) a = b Hi, There is an error. 40% of total work done is (40/100) (a+3b)/10 .Equate this to (a+b)/10. You will get the answer.
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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19 Jun 2014, 19:28
Let me try to answer. The mistake is, Work done by x = (a + b)/10 You will then get b=3a. Substituting in the equations you will get b=3 which is the total number of days X and Y worked together.[/quote] I tried it; however not getting through Equation comes up a follows: \(\frac{40}{100} . \frac{a+4b}{10} = \frac{a+b}{10}\) a = b[/quote] Hi, There is an error. 40% of total work done is (40/100) (a+3b)/10 .Equate this to (a+b)/10. You will get the answer.[/quote] \(\frac{40}{100} \frac{a+3b}{10} = \frac{a+b}{10}\) b = 3a Answer = 3 Sravna: Thank you so much. Kudos to you Now I'll retrospect as to why I failed to get the correct answer & how to avoid it in future
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X takes 10 days to complete a task. Y takes half that time [#permalink]
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19 Jun 2014, 20:50
Dear Paresh, You are welcome. If you know how the given info can be methodically used to arrive at the answer there is not a better way to solve the problem. It can come with practice or with guidance but it is something which can definitely be learnt. All the best.
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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23 Aug 2014, 02:09
The question is much eaiser solved by picking up a smart number. Let's say that Total Work = 100 (divisible by 10, 5 and 4).
The work rate of X = 10 The work rate of Y = 20 (as time is half of X, the rate is twice fatser)
X did some part of work in t days = 10t. The remaining work = 10010t. X and Y completed the remaing work in [(10010t) / 30] days. So
10t + 10 * [(10010t)/30]*10=100*0.4 t=1 The remaining work 90. X and Y worked 90/30 = 3 days.



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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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23 Aug 2014, 06:38
So easy one I think................ cause Let they together done M days. and Y done 60% of the work. So...... M/5=60/100......... M=3 days(simple)



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X takes 10 days to complete a task. Y takes half that time [#permalink]
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28 Mar 2015, 00:56
SravnaTestPrep wrote: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2 B. 3 C. 4 D. 5 E. 6 if 40% is done by X , 60% is done by Y and question tells us clearly that Y joins X and they both continue together , X do not go anywhere once Y joined him, so the time it took Y to complete 60% of work will be the time both X and Y worked together. 5* 60% = 3 days
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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22 Feb 2018, 09:27
SravnaTestPrep wrote: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2 B. 3 C. 4 D. 5 E. 6 We can let the number of days X worked alone = x and the number of days X and Y worked together = t. Since the rate of X is 1/10 and the rate of Y is 1/5, we have: x(1/10) + t(1/10) = 2/5 and x(1/10) + t(1/10 + 1/5) = 1 If we subtract the first equation from the second, we have: t(1/5) = 3/5 t = 3 Answer: B
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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22 Feb 2018, 11:39
t1  days only when X worked t2  days when both X and Y worked together
Given: X's work => \(\frac{t1}{10}\) + \(\frac{t2}{10}\) = \(\frac{4}{10}\) => t1 + t2 = 4 Y's work => \(\frac{t2}{5}\) = \(\frac{3}{5}\) => t2 = 3 , so X and Y worked together for 3 days



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X takes 10 days to complete a task. Y takes half that time [#permalink]
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22 Feb 2018, 11:52
SravnaTestPrep wrote: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2 B. 3 C. 4 D. 5 E. 6 Since X takes 10 days to complete a task, Y must complete the task within 5 days because Y takes half the time X takes to complete the work. If the total unit of work is 50 units, X does 5 units/day and Y does 10 units/day
We are told that 40% of the total work  20 units is to be done by X. Therefore, Y working along with X does 60% of the work  30 units in 3 days(Option B)
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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07 Apr 2018, 06:32
pushpitkc wrote: SravnaTestPrep wrote: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2 B. 3 C. 4 D. 5 E. 6 Since X takes 10 days to complete a task, Y must complete the task within 5 days because Y takes half the time X takes to complete the work. If the total unit of work is 50 units, X does 5 units/day and Y does 10 units/day
We are told that 40% of the total work  20 units is to be done by X. Therefore, Y working along with X does 60% of the work  30 units in 3 days(Option B)hi! can you please explain explain how does the work come out to be 3 days using this method since combined work rate is 15 units per day and remaining units are 30. Hence working together comes out to be 2 days? Thanks!



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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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07 Apr 2018, 15:23
SravnaTestPrep wrote: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2 B. 3 C. 4 D. 5 E. 6 let d=number of days X and Y work together Y's rate=1/5 Y's share of total work=60% 1/5*d=.6 d=3 B



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X takes 10 days to complete a task. Y takes half that time [#permalink]
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11 Apr 2018, 17:13
asfandabid wrote: pushpitkc wrote: SravnaTestPrep wrote: X takes 10 days to complete a task. Y takes half that time to complete the same task. X starts working on the task and later Y joins X. Both work on the task together and complete the task. If 40% of the total work is done by X, for how many days did X and Y work together?
A. 2 B. 3 C. 4 D. 5 E. 6 Since X takes 10 days to complete a task, Y must complete the task within 5 days because Y takes half the time X takes to complete the work. If the total unit of work is 50 units, X does 5 units/day and Y does 10 units/day
We are told that 40% of the total work  20 units is to be done by X. Therefore, Y working along with X does 60% of the work  30 units in 3 days(Option B)hi! can you please explain explain how does the work come out to be 3 days using this method since combined work rate is 15 units per day and remaining units are 30. Hence working together comes out to be 2 days? Thanks! Overall X does 40% of the work and Y does 60 % of the work . IF there were 50 units of work in 10 days X would have completed 40% of 50 which is 20 units of work. Y would have done the remaining 30 units of work. Y would take 3 days to do that or in other words Y worked for 3 days which implies X and Y together worked for 3 days.
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