We are given that $84\%$ of $N$ is equal to $105\%$ of $(N-120)$. We need to find what percentage of $N$ is equal to $192$.

1. Problem Description

We are given that $84\%$ of $N$ is equal to $105\%$ of $(N-120)$. We need to find what percentage of $N$ is equal to $192$.

2. Solution Steps

First, we can translate the given information into an equation:

$0.84N = 1.05(N - 120)$

Now, we solve for $N$:

$0.84N = 1.05N - 1.05(120)$

$0.84N = 1.05N - 126$

$1.05N - 0.84N = 126$

$0.21N = 126$

$N = \frac{126}{0.21}$

$N = 600$

Now we want to find what percentage of $N$ is equal to

1

9

2. Let $x$ be the percentage we are looking for. Then

$x\% \cdot N = 192$

$\frac{x}{100} \cdot N = 192$

Since $N = 600$,

$\frac{x}{100} \cdot 600 = 192$

$6x = 192$

$x = \frac{192}{6}$

$x = 32$

3. Final Answer

The percentage of $N$ that represents 192 is 32%.

Final Answer: E) 32