If p is 500 percent of q, and q is 400 percent of z, then z is what percent of p?

Question

Manish Verma · Accepted Answer

First, we can note that 500% of a number is equivalent to 5 times that number, and 400% of a number is equivalent to 4 times that number. Next, with these facts in mind, we can create two equations:
p = 5q (equation 1)
q = 4z (equation 2)
We can substitute 4z for q in equation 1:
p = 5(4z)
p = 20z (equation 3)
Now, to find out what percent z is of p, we can divide these two quantities and multiply the result by 100:
z/p ✕ 100
Finally, we can simplify this expression if we use equation 3, plugging in 20z for p:
z/p ✕ 100 = z/20z ✕ 100 = 1/20 ✕ 100 = 100/20 = 5
Thus, z is 5% of p.