Problem Solving

The right answer id D 22/15

Work "A" -- Time taken by y&z working together -- A[(1/15)+(1/18)]=1 --> A = 90/11
Same work "A", completed by x in 12 hrs
So ratio = 12/(90/11)=22/15

Ans D

D

Thanks Stuart. Understood why the fraction is flipped. The right answer is 22/15. Cheers!!!

There's a much better and easier way to solve this problem, which would hardly use pen and paper. Here it goes:

Instead of assuming the total word done as 1, which leads us to fractions and then calculations, lets assume the total work to be the LCM of the individual times taken by X, Y & Z.
The LCM would be 180.

Now, the work done by X = 15
the work done by Y = 12
the work done by Z = 10

Thus the ratio of work done by X to that done by Y & Z = 15 : (10 + 12) i.e 15:22
Therefore the ratio of time taken will be 22 : 15

Hope it helps...

Cheers!!!
Umang

if you got this wrong, here's where i tripped up:

1/12T=W
11/90T=W

so we need to find the TIME:
T=12W
T=90/11W

then solve:
12W/(90/11W)
= (12*11)W / 90
= 22/15 W

plug in 1 for W (since it is 1 job)

Y & z can do the job in 1/15. + 1/18=11/90
Thus they can do the job in 90/11 hrs
Thus the ratio is
12/90/11= 22/15
Thus the answer is D

Well no need for such huge calculations. this can be explained very easily !
the above fact means : machine 1 can finish it in 12 hrs.
Machine 2 in 15 and machine 3 in 18 hrs.
So machine 2 and 3 will, combined, take 1/(1/15+1/18) . U first calculate the rate per hour done by both and then invert it so that you whats the total time taken. ---> 33/270.

So the ratio is 12*33 / 270 which gives the desired answer!

OA is 15/22

ie rate of x divided by combined rate of y and z taken individually.

ie (1/12)/(1/15+1/18).

Oops i got that wrong ... its for time... OA 22/15 , thanx everyone

Answer is D

x = 12hrs, y = 15 hrs, z = 18hrs
y and z combined will do 1/15 + 1/18 in one hour which equals 11/90.

x alone will do the 1/12 of the job in an hour.

x:y and z = 1/12 : 11/90 = 15/22. this is the ratio of work done in an hour.

The inverse of 15/22 which is equal to 22/15 gives us the ratio of time it takes printer x to do the job, working alone to time it takes printers y and z to do the job working together.

In 1 hour combined work of y + Z = 1/15 + 1/18 = 11/90
Total time of y + z = 90/11 (reverse the 1 hour number to get the total time)

Ratio of X:y+z = 12:90/11 = (12 x 11)/90 = 2 x 11/15 = 22/15

Ans: D

For those who not having a clarity on the approach . Simple way

Rate of work = work / time
we need to find : x / combined time of y and z

combined time of y and z :

we know individual time , suppose both do a common amount of work w . then

rate of doing w y = w/time to do w = w/(1*y) = w/y

Rate of doing w by z = w/z

Combined rate = w(1/y+1/z)

again rate = w / time , so combined time = w / combined rate = w/w(1/y+1/z)

ie 12/(1/((1/15)+(1/18))

= 12/(1/(33/(15*18)) = 22/15

HOW DID YOU GET THE THE 6, 5 AND 90

camitava wrote:Enginpasa1,
Look if y and z work together, they can do = (1/15 + 1/18) amount in 1 day = (6 + 5) / 90 = 11/90.
so y and z can complete the work in 90/11 days.

On the other hand, x can do the work in 12 day.
So ratio is = 12 : 90/11 = 22/15.

Look the Qs is asking for - 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? So you can not do the ratio with the amount of work, u got, that x and (y + z) can do in 1 hr.

1/12 -> Amount of work done by X in 1 hr
11/90 -> Amount of work done by Y and Z in 1 hr . So u can not do the ratio of these numbers. Got me, Enginpasa1?

The answer is D
;15
12 : (18*15/33) = 22:15