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

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exc4libur
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   06 Apr 2020, 06:17
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


xa+(x+y)b=1
xa+xb=2/5
(x+y)b-xb=1-2/5=3/5
yb=3/5, (1/5)b=3/5, b=3

Ans (B)
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   28 Aug 2020, 00:23
Given: 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.
Asked: If 40% of the total work is done by X, for how many days did X and Y work together?

X takes 10 days to complete a task.
Y takes 5 days to complete a task.

X starts working on the task and later Y joins X. Both work on the task together and complete the task.
Let us assume that X worked for x days and then they both worked together for y days to complete the task

Work done by X = x/10 + y/10
Work done by Y = y/5
(x+y)10 + y/5 = 1
x/10 + 3y/10 = 1
x + 3y = 10

Work done by X = (x+y)/10 = .4
x + y = 4
X & Y worked together for = y = 3 days


IMO B
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   18 Sep 2020, 10:39
I solved this in a slightly different way.

X completed 40% of the work. So, Y completed the 60% remaining work.

Y takes 5 days to complete 100% of work. So, to complete 60% of work, he needs 60*5/100 = 3 days.
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   20 Sep 2020, 07:46
please explain... i am getting ans as 2 i.e. option A
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   20 Sep 2020, 08:46
SVaidyaraman 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


X done 40% of work and remaining work will gonna done by X and Y both.
Since the efficiency of X:Y is 1:2.
So the remaining 60% work will also gonna complete in 1:2 ratio.
That means 20% of work will done by X and 40% will done by Y in perticular time.

Since X require 10 days to complete 100% work, so he will need 2 days to complete remaining 20% of work and so does Y, to complete 40% of remaining work.

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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   15 Oct 2020, 01:00
what a tricky question/. phrasing :/
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   30 Dec 2020, 19:43
I cannot make sense of the answer no matter how you put it. Could you further explain?

Considering the 100 units of work, if A has done 40 of them at a rate of 10 per day= 4 days.
Y came and he does does double, thus 20 units per day. If they are working together, they do 30 units per day. In 2 days they will do 60 units of work.

X works 4 alone. Y joins and together with X finish the job in 2 more days.

What am i missing here?

Thank you,
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   25 Nov 2022, 16:05
Why is everyone solving for time it will take Y alone to complete 60% of work? The question said time taken for X and Y working together to complete the task. The answer should be 2 days not 3.

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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   25 Nov 2022, 23:33
Expert Reply
Solution

Time actually worked by x = ax and by Y = ay
ax is also equal to ax1 + ax2 where ax1 is the time worked by x alone and ax2 time worked together and ax2=ay

ax/10+ay/5 = 1
(ax1/10 + ax2/10) +ay/5 =1
(ax1/10 +ay/10) +ay/5=1
ay/5 =1-4/10 = 6/10
ay=3
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink] New post   26 Apr 2024, 22:32
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Re: X takes 10 days to complete a task. Y takes half that time [#permalink]
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