Working simultaneously and independently at an identical constant rate, 30 machines of a certain type can produce a total of x units of product P in 3 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 10 days? Choose the correct option
A) 41  B) 44  C) 45  D) 47  E) 50

Rationale: "the rate of 30 machines is rate = job / time = x / 3 units per day - - > the rate of 1 machine 1 / 30 * ( x / 3 ) = x / 90 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 90 ) = 5 x - - > m = 45 . answer : c ."
Answer: C