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X, Y and Z together can complete a job in 10 days. The rate of work of

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Bunuel
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X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   18 Jun 2019, 00:23
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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
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C
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   18 Jun 2019, 00:34
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(z+2z+6z)*10=1
z=1/90

So z can complete the job alone in 90 days

Answer is (C)

Hit Kudos if this helped!
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   18 Jun 2019, 00:47
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Bunuel 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


Through rate 1/x+1/y+1/z=1/10; since rate of z=2*rate of y and 6*rate of x from the stem 1/z+2/z+6/z=1/10;Z=90 IMO C
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   18 Jun 2019, 05:30
Bunuel 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


giveb
x+y+x/xyz=1/10
and
x=2/z
y=2*3/z ; 6/z
so total ; 9/z= 1/10
z=90
IMO C
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   18 Jun 2019, 07:30
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Bunuel 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


Given, 1/X + 1/Y + 1/Z = 1/10

The rate of work of X is three times that of Y, which, in turn is twice that of Z
—> X takes 1/3rd time of Y, which in turn takes half the time of Z
—> X = Y/3 & Y = Z/2
—> X = Z/6

1/X + 1/Y + 1/Z = 1/10
—> 6/Z + 2/Z + 1/Z = 1/10
—> 9/Z = 1/10
—> Z = 90 days

IMO Option C

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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   21 Jun 2019, 19:50
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Bunuel 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


We can let the number of days it takes X alone to complete the job be x. Thus, the rate of X = 1/x, so the rate of Y is 1/3x, and the rate of Z is 1/6x; thus:

1/x + 1/3x + 1/6x = 1/10

Multiplying by 60x:

60 + 20 + 10 = 6x

90 = 6x

x = 15

So the rate of z is 1/90, so it takes Z 90 days to complete the job.

Alternate solution:

We can let the number of days it takes Z alone to complete the job be z. Thus, the rate of Z = 1/z, so the rate of Y is 2/z, and the rate of X is 6/z, thus:

6/z + 2/z + 1/z = 1/10

9/z = 1/10

z = 90

Answer: C
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   05 Jul 2020, 14:58
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Bunuel 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


Solution:

We can let n = the number of days it takes Z alone to complete the job. Thus Z’s rate is 1/n, Y’s rate is 2/n and X’s rate is 6/n. We can create the equation:

1/n + 2/n + 6/n = 1/10

Multiplying the equation by 10n, we have:

10 + 20 + 60 = n

90 = n

Answer: C
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X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   05 Jul 2020, 18:34
Bunuel 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


rates for Z, Y, and X are 1/z, 2/z, 6/z
ratio of Z's rate to combined rate=1/9
in ten days Z can can complete 1/9 of job
in 10*9 days Z can complete entire job alone
90 days
C
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   21 Aug 2020, 09:31
Can someone solve the above using options please?
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   13 Sep 2020, 21:47
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

Explanation:
Let Z does the work with rate= 1/z

Then Y will do the work
with rate = 2/z

And X will do the work with rate = =3/y
=6/z



Now X,Y,Z together take 10 days to complete a work i.e

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

1/z+2/z+6/z=1/10

z=90

Hence C is the correct answer.

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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   13 Sep 2020, 22:34
Let Rate of X be Rx..Similarily Ry and Rz. Now as per question, Rx = 3 Ry
Ry= 2 Rz
So, Rx can also be expressed in terms of Rz.
Rx= 3Ry = 3 x 2 Rz = 6Rz
Rate = Work / Time
=> Rx+Ry+Rz = 1 /10
=> 9Rz = 1/10
=> Rz = 1/ 90 = Work done by Z/ Total time taken by Z

=> Total time taken by Z alone to complete the work = 90 days.

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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   19 Dec 2020, 21:44
Let the Rates be the following:

Rate of X = 1/X

Rate of Y = 1/Y

Rate of Z = 1/Z

Working together, they can complete 1 job in 10 days. Add the 3 Rates.

1/X + 1/Y + 1/Z = 1/10


Rate of X = (3) * (Rate of Y)

Rate of Y = (2) * (Rate of Z)

Rate of Z = 1/Z



Rate of Y = (2) * (1/Z) = 2/Z

Rate of X = (3) * (Rate of Y) = (3) * (2/Z) = 6/Z



substitute the Rate of Y and Rate of X in terms of 1/Z ----- in which Z = the No. of Days in which Z can complete the 1 job alone

6/Z + 2/Z + 1/Z = 1/10

9/Z = 1/10

Z = 90 Days
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink] New post   09 Mar 2023, 19:01
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Re: X, Y and Z together can complete a job in 10 days. The rate of work of [#permalink]
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