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# X takes 10 days to complete a task. Y takes half that time

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Director
Joined: 17 Dec 2012
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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, 04:32
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00:00

Difficulty:

95% (hard)

Question Stats:

57% (02:23) correct 43% (02:09) wrong based on 349 sessions

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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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Srinivasan Vaidyaraman
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http://www.sravnatestprep.com

Holistic and Systematic Approach

Originally posted by SravnaTestPrep on 17 Jun 2014, 03:45.
Last edited by SravnaTestPrep on 17 Jun 2014, 04:32, edited 2 times in total.
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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, 04:23
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, 04:33
I have edited the question to remove any ambiguity.
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Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

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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, 06:30
2
1
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, 08:01
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, 01:29
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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Director
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Location: India
X takes 10 days to complete a task. Y takes half that time  [#permalink]

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19 Jun 2014, 01:07
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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Srinivasan Vaidyaraman
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http://www.sravnatestprep.com

Holistic and Systematic Approach

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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, 04:10
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, 06:45
1
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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Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

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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, 18:28
1
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, 19:50
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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http://www.sravnatestprep.com

Holistic and Systematic Approach

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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, 01:09
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 = 100-10t. X and Y completed the remaing work in [(100-10t) / 30] days. So

10t + 10 * [(100-10t)/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, 05:38
1
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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27 Mar 2015, 23:56
1
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, 08:27
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, 10:39
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, 10:52
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, 05:32
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, 14:23
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, 16:13
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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Holistic and Systematic Approach

X takes 10 days to complete a task. Y takes half that time   [#permalink] 11 Apr 2018, 16:13
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