To solve this question, the user needs to know the concept of the work rate formula, which is given by:
work = rate x time
where work refers to the amount of work done, rate refers to the rate at which work is done, and time refers to the amount of time taken to complete the work.
Using this formula, we can derive the formula for this question as follows:
work = rate x time
x = w*r*n (1) # The amount of work done by w workers in n days to produce x toys
y = c*r*t (2) # The amount of work done by c workers in t days to produce y toys
Since the workers are working at the same rate, we can equate the rates in equations (1) and (2):
w*r = c*r
r = w*c/r
Substituting r in equation (1), we have:
x = w * (w*c/r) * n
x = w^2 * c * n / r
Substituting r in equation (2), we have:
y = c * (w*c/r) * t
y = w*c^2 * t / r
Equating the value of r in both equations, we get:
w*c/r = w*c/r
Thus, we can equate the two expressions for r and solve for t:
w*c/r = w*c/r
w*c/(w*c) = n/t
t = n*w*c/(w*c) = n
Therefore, the formula for the number of days it takes c workers to produce y toys is:
y = w^2 * c * n / x
Simplifying this expression, we get:
y*w*n / x*c
Therefore, the answer is:
The Answer is: D