Problem Solving (PS) | Re: When the positive integer k is divided by the positive integ

When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 81.2 , what is the value of n?

A. 9
B. 20
C. 55
D. 70
E.81

Can someone break this down for me please?

Here is a response from Beat The GMAT (/tricky-remainder-problem-t270176.html)

Before I past the question, I am confused with how the user came up with K = 81n +11. Where did the .2 go for thisrepresentation?

"If, when k is divided by n, the remainder is 11, we could say that some multiple of n plus 11 equals k:
xn + 11 = k

If k/n = 81.2, that means that "some multiple of n" (aka the quotient) is 81, and the remainder is represented by the 0.2.

k = 81.2n

and

k = 81n + 11

Now, we can simply set these expressions equal to each other, since they're both equal to k:

81.2n = 81n + 11
0.2n = 11
n = 55"