Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 1/2 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? Options:
A) 2/5  B) 1/3  C) 4/13  D) 8/29  E) 6/33
Now ultimately the speed of every machine is given with respect to Mach O.   So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4   Mach O makes x units in 12 hrs   So, Mach N = 1/2 of O = 1/2*12= 
<gadget id="calculator">1/2*12</gadget>
<output>6</output>
6 hrs to make x units   and Mach M= 3/4 of N = 3/4*6 = 6 hrs to make x units   No they are running simultaneously. Lets see how much each mach makes in 1 hr   Mach O = x/12 units   Mach N = x/6 units   Mach M = x/6 units   In 1 hr, together they make - x/12+x/6+x/6 = 5x/12   So what ratio of this has Mach N made?   (x/6) / (5x/12) = 2/5   2/5ns:2/5=2/5
<result>A</result>
Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 1/2 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?