querio wrote:

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?

(A) 1/2

(B) 1/3

(C) 4/13

(D) 8/29

(E) 6/33

Please solve it and explain it... thanks!

(B) it is
M = time for M to produce the total output T:

=> T/M = output M produce in 01 unit of time

M = 3/4N

N = time for N to produce the total output T:

=> T/N = output N produce in 01 unit of time

N = 3/4O

O = time for O to produce the total output T

Output the 03 machines produce in 01 unit of time = T/M + T/N + T/O = T/(3/4N) + T/N + T(3N/2) = 3T/N

Fraction of the total output is produced by machine N = (T/N)/3T/N = 1/3