Working simultaneously and independently at an identical constant rate, 6 machines of a certain type can produce a total of x units of product P in 5 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 4x units of product P in 10 days?
Choose one
A) 9  B) 10  C) 12  D) 14  E) 18

Rationale: "the rate of 6 machines is rate = job / time = x / 5 units per day - - > the rate of 1 machine 1 / 6 * ( x / 5 ) = x / 30 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 30 ) = 4 x - - > m = 12 . answer : c ."
Answer: C