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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 15 Oct 2017, 05:28
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A
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Difficulty:

  55% (hard)

Question Stats:

57% (02:19) correct 43% (01:10) wrong based on 7 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) 60 days
B) 80 days
C) 90 days
D) 120 days
E) 150 days
[Reveal] Spoiler: OA

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Last edited by chetan2u on 15 Oct 2017, 05:55, edited 1 time in total.
edited the choices

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

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New post 15 Oct 2017, 05:48
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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) 60 days
B) 120 days
C) 90 days
D) 180 days
E) 150 days


As rate is given so lets assume some smart numbers for the number of days required by each to complete the work.

Let \(z\) complete the work in \(12\) days so \(y\) will do it in \(6\) days and \(x\) will do it in \(2\) days (as rate of \(x=3*\)rate of \(y\); and rate of \(y=2*\)rate of \(z\)

So \(x+y+z\) together will do it in \(= \frac{1}{2}+\frac{1}{6}+\frac{1}{12}=\frac{9}{12}\)

or together they will take \(\frac{12}{9}\) days

but it is given that they took \(10\) days

So, together they took \(\frac{12}{9}\) days, when \(z\) took \(12\) days alone to do the work

Hence together when they took \(10\) days then \(z\) will take \(=\frac{12}{12/9}*10=90\) days

Option C

Last edited by niks18 on 15 Oct 2017, 05:54, edited 1 time in total.

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

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New post 15 Oct 2017, 05:54
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) 60 days
B) 120 days
C) 90 days
D) 180 days
E) 150 days


hi..

Although the Q is correct, the answer choices are not given in ascending or descending order, a must requirement in all GMAT questions, so editing the choices

another way :-

Since we are to find time taken by Z, lets convert each in terms of Z..
Quote:
The rate of work of X is three times that of Y, which, in turn is twice that of Z.

Y's rate twice of Z means each Y works equal to 2*Z..
X thrice of Y means \(X = 3*Y = 3*2*Z=6*Z\)

so X, Y and Z combined means 6Z, 2Z and Z or 9*Z, so 9Z did work in 10 days..
therefore Z will do it in 10*9=90 days
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 15 Oct 2017, 07:39
I have a easy method, you may consider...
let, x do the work in x days
y do the work in 3x days
z do the work in 6x days
So,
X's 1 day's work is 1/x part
Y's 1 day's work is 1/3x part
Z's 1 day's work's is 1/6x part
So, (X+ Y + Z)'s 1 day's work = 1/x + 1/3x + 1/6x
Again,
(X+ Y + Z) do the work in 10 days
so, their 1 day's work is 1/10
According to the question,
1/x + 1/3x + 1/6x =1/10
Solving this we can get x=15

So, the number of day by z to do the work is = 6x
--------------------------------------------------- = 6 * 15
--------------------------------------------------- = 90 days.

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

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New post 15 Oct 2017, 07:52
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) 60 days
B) 80 days
C) 90 days
D) 120 days
E) 150 days



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Re: X,Y and Z together can complete a job in 10 days.   [#permalink] 15 Oct 2017, 07:52
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