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X, Y and Z together can complete a job in 10 days

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X, Y and Z together can complete a job in 10 days [#permalink]

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New post 28 Dec 2017, 10:49
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Question Stats:

75% (02:06) correct 25% (02:18) wrong based on 16 sessions

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X, Y and Z together can complete a job in 10 days. The rate of work of X is three times that of Y, which, in turn is twice that of Z. What is the time taken by Z alone to complete the job?
A) 30 days
B) 60 days
C) 90 days
D) 120 days
E) 180 days
[Reveal] Spoiler: OA

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Re: X, Y and Z together can complete a job in 10 days [#permalink]

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New post 28 Dec 2017, 11:24
Given

1/x + 1/y + 1/z = 1/10

1/x = 3/y & 1/y = 2/z

hence

3/y + 1/y + 1/2y = 1/10

9/2y = 1/10
y = 45 & z = 90

Answer = Z takes 90 days to finish the job
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Re: X, Y and Z together can complete a job in 10 days [#permalink]

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New post 28 Dec 2017, 11:52
souvonik2k wrote:
X, Y and Z together can complete a job in 10 days. The rate of work of X is three times that of Y, which, in turn is twice that of Z. What is the time taken by Z alone to complete the job?
A) 30 days
B) 60 days
C) 90 days
D) 120 days
E) 180 days


Let RX = rate of X
RY = rate of Y
RZ = rate of Z

RX = 3RY & RY = 2RZ & then RX = 6RZ

Apply in formula:

Rate * Time = Work

(RX + RY + RZ) 10 = 1

From above:

6RZ + 2RZ + RZ = 1/10...........9RZ = 1/10.........RZ = 1/90

Inverse of the rate of Z will yield the time Z takes to complete the job

Time of Z = 90 days

Answer: C

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Re: X, Y and Z together can complete a job in 10 days [#permalink]

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New post 28 Dec 2017, 18:53
Let X complete the work in x days, Y in y days, Z in z days
Since all 3 complete the work in 10 days:
(1/x) + (1/y) + (1/z) = 1/10

Rate of work of X is three times that of Y, which, in turn is twice that of Z
Here we are talking about "rate of work" i.e. per unit day (whenever its rate of work the denominator needs to be time in this case 1 unit of work per day)

Thus, (1/x)=3(1/y)
which in turn - we are talking about rate of work of y
(1/y) = 2 (1/z)
=> (1/x) = 6(1/z)
Subsitute these in the original equation. solve for z:
6(1/z) + 2(1/z) + (1/z) = 1/10

(1/z)*(6+2+1) = 1/10
=> (1/z)= 1/90
z= 90 days

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Re: X, Y and Z together can complete a job in 10 days   [#permalink] 28 Dec 2017, 18:53
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