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

Question

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

niks18 · Answer

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

chetan2u · Answer

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..
 
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

raki99 · Answer

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.

Bunuel · Answer

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

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