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 2 / 7 the time it takes machine o to produce that amount of units . if all 3 machines are working simultaneously , what fraction of the total output is produced by machine n ?  Choose the correct option
A) 1 / 2 B) 7 / 13 C) 4 / 13 D) 8 / 29 E) 6 / 33

Rationale: 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 = 2 / 7 of o = 2 / 7 * 12 = 24 / 7 hrs to make x units and mach m = 3 / 4 of n = 3 / 4 * 24 / 7 = 1 / 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 = 7 / 24 units mach m = x / 6 units in 1 hr , together they make - x / 12 + 7 / 24 + x / 6 = 13 / 24 so what ratio of this has mach n made ? ( 7 / 24 ) / ( 13 / 24 ) = 7 / 13 ans : b = 7 / 13
Answer: B