ration to x :(y+z)= 12/15*18/(15+18)
=12*11/90
=22/15

Combined time for y and z = ab/(a+b)=90/11

x : (y&z) = 12 : 90/11 = 132 : 90 = 22 : 15

I fell for the trap answer C.

Can it be fair to say that every time we are given a time problem and solve for the rate, all we have to do is take the inverse?

Answer is D)

x does 1/12 of the job in 1 hour.
y 1/15
z 1/18

y + z = (1/15) + (1/18) = (33/270)

x/(y + z) = (1/12)/(33/270) = 15/22

These are the rates, so the time is in the ratio 22/15.

Common-sense check: 33/270 > 1/12, so y + z is faster than x, so x must take more time!

Quite easy.
Speed X = 1/12 hr^-1
Y+Z = 1/15+1/18 hr^-1 = 11/90 hr^-1
Ratio = 12 / (90/11) = 22/15
(D) is answer.

IMO : D

Required: Time spent by X/Time spent by Y and Z

Time spent by X =12

Time spent by Y and Z = 1/(1/y+1/z)= 90/11

Ans: 12/(90/11)= 22/15

4/11

22/15... EASY

I also ended up with 15/22 (c)

But I realized that from my calculation, I need to reverse the result, because the question is asking the "time".

So the correct answer is D

working alone, printers x,y, and z can do a certain printing job, consisitning of a large number of pages, 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer x to do the job, working at its rate, to time it takes printers y and z to do the job, working together at their individual rates?

a. 4/11
b.1/2
c. 15/22
d.22/15
e.11/4

Tx=12, Ty=15 & Tz=18
Tyz=Ty*Tz/(Ty+Tz)
Tyz=15*18/33
Tx/Tyz=12*33/15*18
Tx/Tyz=22/15

Hence, Option D is correct

working alone, printers x,y, and z can do a certain printing job, consisitning of a large number of pages, 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer x to do the job, working at its rate, to time it takes printers y and z to do the job, working together at their individual rates?

a. 4/11
b.1/2
c. 15/22
d.22/15
e.11/4
solution:

we have to find x : y+z
therefore
1/12 : 1/15 + 1/18
1/12 : 6 + 5 / 90
1/12 : 11 / 90
90 / 12 * 11
we get
15 / 22
now just receprocal it
22 / 15
D is the right choice

x takes 12 hrs to complete a job
when y and z work together -
rate of working for y is 1/15
rate of working for z = 1/18
when both y and z work together- rate is 1/y+1/z = 1/15+1/18 = 11/90

hence y and z together can complete the task in 90/11 hrs

ratio of x :(y and z)=12/(90/11) = 12 * 11/90 = 22/15.

X's rate: 1/12
Y's rate: 1/15
Z's rate: 1/18

Find ratio of X's rate to Y+Z's rate


Y+Z's rate:

1/15 + 1/18 ==> 18/270 + 15/270 ==> 33/270 ==> 11/90

11/90 = Y+Z's amount of job done in 1 hour, therefore 90/11 = hours to complete one job


Now find ratio of X to Y+Z

12/(90/11) ==> (12*11)/90 ==> 132/90 ==> 66/45 ==> 22/15


answer is D, 22/15

X:Y:Z
12:15:18


= 4:5:8

X/h: 1/Y+1/Z
=4/1: 1/5+1/6
= 4/1: 6+5/30
= 4/1: 11/30
=4/1*11/30= 44/30=22/15