Machine M can produce x units in 3/4 of the time it takes machine N to produce
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?
please explain, thank
LG FLT2 Q28
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.
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.
- Rep Power
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)
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
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!
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
9/24=3/8 = 1/t
t= 8/3 is the time taken by 3 machines
N's share = 8/8/3 = 3
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