Machine M can produce x units in 3/4 of the time it takes machine N to produce

[nh8404052006]

Machine M can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

Ans.:

SPOILER: 1/3

please explain, thank
LG FLT2 Q28

[Shooter]

Let O takes n hrs
then N takes 2n/3
then M takes 3/4*2n/3 = 1/2 hrs

I'll take n=6 as we will get an integer for all the three machines.

Hence O=6;N=4;M=3

All the machines working together = 1/6+1/4+1/3 = 9/12 = 3/4

Hence it takes 4/3, which is 1/3 of N.

Hence 1/3

[cramya]

Take O as the base since N's rate is given in terms of O and M's rate is goven in terms of N(which can be expressed in terms of O)


Let O produce x units in 1 hour so O's rate is x units/hr

N' rate is 3/2*x( since N produces x units in 2/3 hr so in 1 hour 3/2*x) = 1.5x

M's rate is 2x (4/3rds of N's rate = 4/3*1.5x)

Working simultaneously:

Combined rate * no of machines(when working together the three machines are treated as 1) * time = work

(x+1.5x+2x)* 1 * 1 = 1

x = 1/4.5 = 2/9

N is 1.5x = 3/9 = 1/3


Check:

M will be 2*2/9 = 4/9

2/9+4/9+1/3 = 9/9 = 1 unit or 1 job or 1 work

Hope this helps; let me know if u need further clarification! Good Luck!

[kool_sunny]

Thanks Ramya and Shooter

[genius_in_the_gene]

Let O produces x machines in 12 hrs.
12 is a good number to choose as it is divisible by 4 and 3.

So N will take 2/3 *12 = 8 hrs

And M will take 3/4*8 = 6 hrs

together they will take
1/12+1/8+1/6 =1/t

9/24=3/8 = 1/t

t= 8/3 is the time taken by 3 machines

N's share = 8/8/3 = 3